symbolicsolve.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "symbolicsolve.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNpayTg5LY5klJ4G3nZobQl",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sujithgunturu/Math799/blob/master/symbolicsolve.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K8t90IxOHxi9"
      },
      "source": [
        "from sympy import *\n",
        "init_printing(use_unicode=True)"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dBW-TEQoH1wb"
      },
      "source": [
        "S_xl, theta_vr,theta_vd, theta_vo, theta_vs, theta_vq, theta_ps, theta_a, theta_pr, \\\n",
        "theta_pm, theta_tr, theta_td, theta_t0, theta_alpha, theta_el, theta_k, theta_sr,\\\n",
        "theta_sm, theta_rue, theta_m, theta_gx, theta_gb, theta_ts, k_i, k_m, k_e,t\\\n",
        "= symbols('S_xl theta_vr theta_vd theta_vo theta_vs theta_vq theta_ps \\\n",
        "theta_a theta_pr theta_pm theta_tr, theta_td, theta_t0, theta_alpha, theta_el, theta_k\\\n",
        " theta_sr theta_sm theta_rue theta_m theta_gx theta_gb theta_ts k_i k_m k_e t')"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4fLktaAyH5kE"
      },
      "source": [
        "S_vt = Function('S_vt')\n",
        "S_lt = Function('S_lt')\n",
        "S_at = Function('S_at')\n",
        "S_wt = Function('S_at')\n",
        "S_bt = Function('S_bt')\n",
        "S_yt = Function('S_yt')\n",
        "S_gt = Function('S_gt')"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ud4NWFs9H9nh"
      },
      "source": [
        "from scipy.interpolate import interp1d\n",
        "import numpy as np\n",
        "from sympy import *\n",
        "# DataPointsDomain = np.linspace(0, 10, 3, endpoint=True)\n",
        "# DataPointsRange =  np.cos(-DataPointsDomain**2/9.0)\n",
        "# average_daily_temperature = interpolating_spline(2, t, DataPointsDomain, DataPointsRange)\n",
        "# average_daily_temperature"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nZxtl-PpH_kW"
      },
      "source": [
        "t = Symbol('t')\n",
        "W_at = t**2\n",
        "W_pt = t**2\n",
        "\n",
        "W_st = t**2\n",
        "W_nt = t**2\n",
        "W_ht = t**2\n",
        "\n",
        "W_pt2 = t**2\n",
        "W_st = t**2\n",
        "W_wt = t**2\n",
        "\n",
        "W_rt = t**2\n",
        "W_xt = t**2\n",
        "\n",
        "import numpy as np\n",
        "from scipy import interpolate\n",
        "import pandas as pd\n",
        "df = pd.read_csv('/content/Weather_data_2020.csv')\n",
        "x = np.linspace(0,4, 4, endpoint=True)\n",
        "\n",
        "\n",
        "# DataPointsRange =  np.cos(-DataPointsDomain**2/9.0)\n",
        "# average_daily_temperature = interpolating_spline(2, t, DataPointsDomain, DataPointsRange)\n",
        "# RELHUM2MAVG\n",
        "\n",
        "# y = df[\"RELHUM2MAVG\"][:4]\n",
        "# W_ht = interpolating_spline(2, t, x, y)\n",
        "# #W_ht = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# #WSPD2MAVG\n",
        "# y = df[\"WSPD2MAVG\"][:4]\n",
        "# W_wt = interpolating_spline(2, t, x, y)\n",
        "# #W_wt = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# #PRECIP\n",
        "# y = df[\"PRECIP\"][10:14]\n",
        "# W_rt = interpolating_spline(2, t, x, y)\n",
        "# #W_rt = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# # (TEMP2MAVG)\n",
        "# y = df[\"TEMP2MAVG\"][:4]\n",
        "# W_at = interpolating_spline(2, t, x, y)\n",
        "# #W_at = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# #SR\n",
        "# y = df[\"SR\"][:4]\n",
        "# W_st = interpolating_spline(2, t, x, y)\n",
        "# #W_st = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# #PRESSUREAVG\n",
        "# y = df[\"PHOTOPERIOD\"][:4]\n",
        "# W_pt = interpolating_spline(2, t, x, y)\n",
        "# #W_pt = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "# #PHOTOPERIOD\n",
        "# y = df[\"PRESSUREAVG\"][:4]\n",
        "# W_pt2 = interpolating_spline(2, t, x, y)\n",
        "# #W_pt2 = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "# #TEMP2MMIN\n",
        "# y = df[\"TEMP2MMIN\"][:4]\n",
        "# W_nt = interpolating_spline(2, t, x, y)\n",
        "# #W_nt = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n",
        "\n",
        "\n",
        "# #TEMP2MMAX\n",
        "# y = df[\"TEMP2MMAX\"][:4]\n",
        "# W_xt = interpolating_spline(2, t, x, y)\n",
        "# #W_xt = interpolate.interp1d(x, y, fill_value=\"extrapolate\")\n"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SuyRr20U1UjS"
      },
      "source": [
        "theta_vr = -0.28\n",
        "theta_vd = 5\n",
        "theta_vo = 4\n",
        "theta_vs = 1\n",
        "theta_vq = 42\n",
        "theta_ps = 0.8\n",
        "theta_pr = 0.44\n",
        "theta_pm = 10.67\n",
        "theta_tr = 0.14\n",
        "theta_td = -7.6\n",
        "theta_t0 = 24\n",
        "theta_alpha = 0.30\n",
        "theta_el = 18\n",
        "theta_k = 0.75\n",
        "theta_sr = 10\n",
        "theta_sm =35\n",
        "theta_gx = 45\n",
        "theta_m = 60\n",
        "theta_gb = 20\n",
        "theta_ts = 15\n",
        "theta_rue = 1.15\n",
        "theta_a = 36\n",
        "S_xl = 150\n",
        "# wrong, added for time being\n",
        "k_i = 0.45\n",
        "k_m = 1.3\n",
        "k_e = 0.2"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7hx0h-8nwvrx"
      },
      "source": [
        "1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "id": "sbTbahKWIGJw",
        "outputId": "ca885778-7051-4720-a428-b3a208ed4903"
      },
      "source": [
        "dSvt_dt = S_vt(t).diff(t)\n",
        "CV = Eq(dSvt_dt, (1 + exp(-1 * theta_vr * theta_vd))/(1+ (exp((-1 * theta_vr * (W_at - theta_vo + theta_vd)))) + ((exp( (theta_vr) * (W_at - theta_vo)  - 1)))))\n",
        "CV"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{vt}}{\\left(t \\right)} = \\frac{5.05519996684468}{1.32312981233744 e^{0.28 t^{2}} + 1 + 1.12749685157938 e^{- 0.28 t^{2}}}$",
            "text/plain": [
              "d                                 5.05519996684468                     \n",
              "──(Sᵥₜ(t)) = ──────────────────────────────────────────────────────────\n",
              "dt                                   2                                2\n",
              "                               0.28⋅t                          -0.28⋅t \n",
              "             1.32312981233744⋅ℯ        + 1 + 1.12749685157938⋅ℯ        "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DoGRyrBAww7q"
      },
      "source": [
        "2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 93
        },
        "id": "S_OfyT_4HOZ8",
        "outputId": "52715283-7757-46b4-b8d2-c0fb24aa726e"
      },
      "source": [
        "f_vt = 1-theta_vs*(1- 1/(1+exp(-10/theta_vq*(S_vt(t) - theta_vq/2))))\n",
        "f_pt = 1 - (1 - theta_ps * (1- (1 / (exp(-100 * (( S_at(t)/theta_a)-1) ))) )) * (1/(1 + exp(-theta_pr*(W_pt - theta_pm))))\n",
        "d_tt = (1 + exp(-1 * theta_tr * theta_td)) / (1 + exp(-1 * theta_tr *(W_at - theta_t0 + theta_td) + exp((theta_tr * (W_at - theta_t0)) -1)))\n",
        "dSat_dt = S_at(t).diff(t)\n",
        "PA = Eq(dSat_dt,f_vt * f_pt * d_tt)\n",
        "PA"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxAAAAAyCAYAAADMdT1dAAAABHNCSVQICAgIfAhkiAAAH6tJREFUeJztnXfcFNXVx790FCxgR4mAYo2IosSeR2Mjdo01oo/GFrvR5LXFl9hj1Kixa/TRGEuMJdaoqGhQDIpC7B2jKDZibCgW3j9+d969O3tn5s4++7AC5/v57Gd3Z+7ce2Z258y95557DhiGYRiGMTfRp9kCGIZhGIZhGEY9tADdmy1EA9kSeBF4Gdgno8wRwLPAc8B5QKeCOkcAlwE3AD9C1+xh4GL3uQdwAXAOcBUwX05dZ7vyV7jv2wA/9vbvC9wCXA6sViBXwgBX3/Xetl5Am5N7t8D3esm7vv2BMei6/gvYsR3t1MvaTWjTMAzDMAxjrmEDYPtmC9FAugIvAUsCvVFHd6FUmUWAV4GeQBfgEeI7nX2AS4AfAncDVwKD0ADgmIjjFwLORJ3wscChToY/emX+ACyBOvx/ipQrwR9AjEQDH9DAJ/09RKt7ZVF0fZcAhrrPiwNT0HnMSvoDB83iNg2jKXRutgCGYRjGXMf8wB7Azc0WpIEMRzMLU4BPUSd/00C5rmgA0c293nPbBwN3AhPQDMOiqeOOQbMO/0Cd8aOB/3Xf50cd/u0C7a2IOtZrI+v8B8DVaPbjG6CvK9cdWMrVeTTqpCesCtyRenXLvBKq5033+ZvA93oour7vABPd56noPPsya3kT+ArYeBa3axiznK7NFsAwDMOY6zgBucnMSfRDnduEKcha7vM+mgX4N/A1GhC8ityKLgT2At4CDgD2A052x50E3Ac85dX1H3fcJ2hw0R24C7kgDUSDjI/QLMVU4HP3fQhy8UmYgYyJP0SuSLc7uY/3ykxCMxexvIUGDc+4utPf6yHm+iYMQ7Mrb2bs70iuAP4G3A/MbEL7hjFLsBkIwzAaxUGoY/Kxe40Dtig4pgvqHL0OfOHeT6bauDEf8u9+A5gOPAqsmapnMnpYp193lqgjRv6YekYF5Jja4DoSDqRy7SYA66f2bwDchjpbMwm7iMSUmRyQx7++sfWArMLrAI/VIcfsTh/UER+AOr/roPPeFlgZWfYnAochSzbA3sBWwA5oULENcCmacbjQvc5D7k2numOWQf+txdGg4XK0bmAA+h/t78okfIvWV3yMBjVnAKdFntOC7pg1gKPctpuBnYCL0G+a/p7Q3Z3vROBE90q+17s2pi+aYdmvzuPby9foXmzPWg/DMAzDmGvYBlk9lwWWA05BnaAhOcccC0xDHaQBwNbIsvprr8wNwPNoweiyqHP9X6qtj4ugzlLyWg11ivYsUUeM/DH1jAJeSMmzSIPrANjZybcvclP5A3Lt+J5X5seoU/kTZIFupZaYMkXXN7Ye0KBnVJ1yfJdZB1n/E86hthO5I1rwnPBL4Fdo0LxrA2X5FfBzV+eBwLrIYPjHVLn+VGY5zm9g+/XQSv5vHnN9eyD3r5GNFKwOlgMeb7IMhmEYhjHbMg1ZO7O4A0WO8bnKbQeYB1n0tkmVmUCl4xPiOGR5nacddUC1/LH1jEKuGiEaUUfCP1FUG5+XybYcf0pxpzymDFRf37L1jEbuMo2Q47tEV3T98xZRr4XckJJF1Hei/8LBKEpRQt6guz20oE52whrUDkybRSvFi6jzrm8n4DrCg9Nm8AFyJTOMORJzYTIMoyPoAuyCHvSP5pQbC2wIrOC+rwRshHy5QZ2GLshFx2c6sF5GnZ2AnwHXuHL11BGSv0w9g4C3kXvR9e57o+oAuXcMA+5NHXMvstR2JOnrW4ZuaDHvpEYL9R3ga+BI4EHkgnMW8KHblyzufQz9t59C7nKvIpeeK5Er0Avo2uzeQTKOAb70vj+B1mXMDhRd33XRrNy2VNygVpn1Yv4/49GAzTAMwzCMAlZB1uOvkYW6aA1EJ+Qq9C1yx5lJ7azAoyjSzJKo8707iuTyYkadm7p6Vq2jjiL5Y+oZgfy9h6BoLGOQ3/lCDayjnzvHDVLynRA4p4RGzUCErm9sPSsgF7UiZscZCMPwORv4fbOFMAzDMIzZge7Ir38YcqX5APh+TvldUKSUXVDnfSRyG/qZV2YZ4CHUaf0aWfauQesIQtzoyvjE1lEkf1lZQLMY7wG/aGAdzRxAhK5vbD2bIyt7EUVynEx4Ubf/aoloxzA6ihOAW5sthGEYhmHMjoymduGmz5so4ozP8cArgbK9ULIo0ELkOwNlFkVhKffNaC+mDp8s+cvW8yCKQNOoOrqjwUc62+4FaHASohEDiKLrW1TPzsCTBcfGyLEwms3Ie80b0Y5hdBSHAA80WwjD6CgsD4RhGB1JZ6oXbaaZl9rEUt8QXp/1mXv1ATZDkWbStCIf7+sy2oupwydL/jL19EQd2gcbWMcMtPB6EzQjkLAJcFNOPe2llfzrW0R35K7WXj5wr7JYXH6jo+iU+v4Z9YeiNYw5jgNQFATDMIw0p6M8BAOQO9JpqLM4witzMNUuLG0oydQW7rjt0KLOs7wym7k6BqIO8kS0GDWdCbcT8BK1kYli64iRP6aeM1GUoYHAD1BEqY+BpRtYB8iaPwPYB4VxPRdZ7v0yvVEW4qEoNOoJ7vP3SpaB/OsbW88OZD9DYuUwjGayPdINPyoodyBwT8eLYxizBxdTbe0yDMNIaEPJ0b5E/vqjUWfZZxTVVuB0UrXXUC6Anl6ZnVC0mi+Bd1C8+gUC7W/o6h4e2BdTR4z8MfVcj6InzUBJ0W5C0aUaWUfCgSjJ25doRiK9JqKF8PqAtpJlIP/6xtazHtkzB7FyGEYz6ON97kexG98xKKGdYRjISnZss4UwDMMwZksWQ2s3zLXDmNX0QoPRywhnie6JcqtsnvH9CvfeDTiJ4v/w+WgWzTDmSPLyQAxF/rbTgaeR1WkVKvGsDcMwDKMM76KF80ObKMMtKJTsXzuoni1RJKyXkXuZz1HAsyhJYCjXw4IoN8NEVyaxci9PJbfBRPRc3tbtG4ie1c+hZ3Wvgvay2qj3nELt58mbdQ3yfpfJKG/GRGrXEsWyPQpWsC+1iRxBOSZuyfi+JcoufShwInLnG1bQ3opoAGIYcxWDgf8in+BlkX/yZDSd3K95YmVyFXI56FVU0DEMnUtaERqGYRgdy0WoI9YsWoCtKB5AtJIfCSpUT1e0TiSULXkVFIGqJ8rg/RjqzPt0oRI9qhdKIpjOZt0buYElz7uH0NodgL5UgqNktZfXRtlzyms/JG/eNQi1nTDZ1RPDqmjNkP/qhlyKkpDM16aOWQvYE/3em2d83y+yfZBxdgrxfRLDmO3ImoE4H4UUPBqFU7wTuA910t+OqLcF3aCTUcbVj5Hl4lbgiJx262FNFDv+dBT1wOcINFBIT1dOcLKcRLxSMgzDMNrP1WjxeLMYA3zSQfUMR9b1KWhB+90o8R7IIj0OPROno4zTm6eO/wYtIAdF/+pEbXSfrYH70fNuZZSA8R9u3zTkIpbXXl4bZc8pr/2QvHnXINR2EYNR/2QC8DAKMzwJzRj4r69QsIal3HHpPshGwGqor7Bv4PsQNAMSyw+AsdT2SQxjjiHUke+PlEM6g+JXFLsvdQEuRVOMW6Hpu/PctpeRojiSxoTxSzgFDVDSMdahMsU4IbDvNGBxmmsJMwzDmNsYhzqs/ZstSAfQD3W0E6Ygyz3IZacFWdz7uM9LUsuCqBP8FvA7ahed74RccUAd6E+B25Fl31+jmNdeURux55TXfkje2GuQZiaa6Xgc+Knb1gO4ENgfPeuvJX+W4GYny0XAbWhBf5Kw8lTgcFfHZYHvU107y0TIipPxvMiyhjFbEsoDsRqyUExKbV+d7ARFCceh0fptwB7IDcqnr6unUSwHbAxcjqwZaYYh5fZSYN94FE5yfzR70chBjWEYhpHNsaiz9+tmC5KiO5Us233d++HufTiKilUvz6FO5QPo2fgYtTlQAD5CbjiLoU7vX9HaEYD5gXVQ5nbQM3x9tKbkPeDvqJN9X0F7eW2UIa/9kLyx1yDNemjgsgSKjvY0ms1YGbkogQYUbTl1fAbsndo2NvU9fbz//bYIOUGDo0WARyLLG8ZsSWgGYiaaSfCTJ62PpuSeyqmrExVr/v7UDh5A05ujy4uZyd6u3RtS209H57ECclH6lkpIwJFeuetRjPFmTqcbhmHMbfwLdcaXa7YgKWZQyUVxApVcFEOJGzy8TbVFfUmq3X4vQUa0DdGsfl5epXeRIW99b9s2wL3IBQjUqX4CLUz/EriL6gXqRe2F2ihzTkXtp+WNkSlEMgPyjmtjdbSe4kgqv8+KwG8j6upoDkbrLQxjjiY0gHgCKYIz0XTdFsA1bl+eC9P8VBZWfdUoAQvYGFkvHkttfxItrAZ4FPiN9xrjlUssBDaAMAzDmLWcjBLqpX38Z2fGo4W6yYLjEVQnE1vUvS+PZjTSicYWQ7lRQLlBNkCLlhN8dyCQtX9R5A7U2ZV/vqC9ojbKnFNR+2l5s2TKo5cnb2+0PuFZ5Fbk52kZUlDPrGBd1B95rdmCGEaz2JVKYqekA/4ZxYuf30RW/ieRb+FS+cXbRS+0WOvpjP37OVnyfCIXcGXG55RJOBwlwYp9bYthGIaRR0/CrrQdyWiU7fxztAZg7YxyreRHYcqqZ2vkNvsKtc+fcciN53Gqw4Amxrnh7vMkNEuzv1dmATRjkM4/MAI9B58Bzo5oL6+Nes4pq/0sebOuQVbbg5ysk1wbh7ntvVAwlBfcvjNoPumoWoZhRLIOUjB+FtE3UAbr1Rrc1nKu/nsz9l/s9q9RUM90ZMkoYjLhLKlZr7aIOg3DMAzDMAxjrieZxjwFLVD6CnWov6VcHGWf31E7zbm2qzc9PZowHvms9sjYnzCF2rBzhmEYhmEYhmE0ib4o7vdMtLC6Hn/Xh1DOBp+hrs6/Bcp3RTMLMVmzp9GYmOCGYRiGYRiGMceTdOZnNqieLPoD/3afFwY+9PYdjxZaDUKd/juBn7vP3VEY1m5e+eeBlajEpn4EhXjzGYJ8Iq+kNmybT2c0+/A6xfGdD6ecf+NE5J8Zor3X2zAMwzAMwzDmaIajTvOH1A42RqHIBUujqEpTqIRA64wWWc10dSyOoj3g6nkPLbpKs4c75pACuVZ05W6KOIfJ2BoIwzAMwzAMwyjkAIrjNO+OOv+hmYhByBo/k7ikQZdSCcEKSkP/cUbdf3X1LpvafoTbvmdBW3u5cgdHyGUYhmEYhmEYs5rtgdOAHzVbkDJcDNzoPocWMwM8SCXi0p9QGvjzUFbKr92+C1CCOp/+rtzTaC3Cp2jR9SlemV8D/8iQbVdX90Gp7Ru47W85mUcBOwaOv87J1z+jfsMwDKPx9EC5BQzDMIxs+nif+wH7NkGG1es98DHgWPc5tJgZlKX6JNTRfwNlnfwcxY2+gnCc7YVQ+NS/oGQwK6PM0Z9Q3dm/CQ0yQnRHcab/Gdh3MEqO8wUaTJyS2r8AWmeRtU7BMAzD6BgOp3ptm2HMKYwALkMRImcra7HRIfRCLu2XAbt52weg/vH13raeqD+7ubftCvfeDfWz03lVZgW7Up2NPshQNJswHc0KDEcJ5LZGIVF9H//n2inQHsBHVLsm7enqHuxtewXYJ6eeY9wxZfNMHOKOSy/ANgyjMWyJBvEvU3sP90dZ4Z9Dyax8o8GCwBPI9fEZqi0uR6AstM8hw0KiP7LaOsqVfwa5WvpMdm1PRHovT656ZKpHrjIy1StXf+AWd9wrVB5QefRGib6SOgah5wLIQnZnRB0JQ1CiUcOYleTpI59bgP8gF+k08yIj6ZneNv9e8OkDXFKXpPGyZpULnUOWHlke6Y/kNR0lws3anhDSL2X1UV4bA5EOfA71R3ulzj30W5TRq3myZh2TdR55jESDSginHfAHEMcBR1MZQGyJ0iEcityXTiY78WVH0gP4bV6BwSjM6uloTcEWVBYO9yN7MXO9bIHch7Zz7R0CvEPteofJ6A/Sj3AUpJ7oT3R7ibbnAd4mrCAMw2g/XdEM5JKo8/kimnVMWAIZLED6ZAqVB0QX9HDAbXvdHbsI8Cq657ugCGxr57S1CvCkKz8Pmk31dchkV94nS66yMuVdgzy5yshUz7XCfd7Mfe6EotoVcTjVeXwOQg+6hEuJf7BdjWXsNWYtRfrIpwXYinD/4BTUCfQ7rel7IeEMsg2brWRnOY+VNa9c6Bzy9EhCb+CDiO1Z+qUefZTVxkPA+u5zX2oz1qd/i7J6NUtWco6JOY80x1Bx17w2sD8ZQKyFjOitVAYQa1F//rRGcwmwmL+hs/f5fGRFOhpZpe4E7kORjt5Gf75PUPr5qWh02x7ucgJdBTyKBjB/RiM+P8zpccAuaD3DaYF6vkAjvCeo/dNnMQA98I6qQ+5G0ge5YBWFkDWM2Y3hyEozBa1tuhvY1Nv/DpU8LVPRg6Ov+/4NcoEEWT46UTEqdEXKu5t7vZfT1orAOKQjpqPQzv7UcIgsucrKlHcNysrVyGvVE1gTPfggfjZ5Nyo5d36IptJ/BjyF9O5taJo74UbgyEA9XZDB6KOINg2jURTpI58xhHNDDUZu1nd720L3Am7bfW5bR8maVy50Dnl6JGFr4H7keVK0PaRf6tGToTZWRuthk/Wv06hO+Bv6Lcrq1TxZ88g6j8Go3zwBeBhY1G1/C1jKffb73Gk2QgPO3ajMhgxBfeLvAhNJXc/kZPqjP97vUwd8ReUPtxr6QRqVwyBZ/Dw/utCHog592qXoz+jid0b5IUI8DPyG2j99Fs+jhdWTywjcARyLBlKvuu8boAfxFHR9Wjuo3bLtJG5i56e2d0GK8nV0076OptjSloKy9cbIdxC6sT52r3FoVqtsPaOoDcE71ds/H3AOmuWajga7a9bRDsCBVK7VBCrWlYRj0AD9YxSe+HZqF5oWyTs5sH8mFReTov2NIsnTkjCFbB/KYei/9Ka3bUGkb5JACB+ga3ImyinzNnKpeTWnrWeQJW5BNFhvSckwE1m5Hgd+GiFXGZnyrkGeXGVlKivXF+g//AKafh9KNskscw9keXrXfX8I3XuboOfCZ8jyt4537InI+LNAqs7ve/UkxOiRmPs9jyxdE3PPxeiAGPliz2EJZFh7H12P51BHFRqj0yYH9qd1QKysRTotpq0ieRtBGX2UxZlUQswnhO6FvZH1fwfqsx7HytqecwrpEVBOrpCbTXp7nt4rqydDbQxGg6LbkW45NlU29FvUo1dDspJzTNZ59AAuBPZH1/ZaKr/9ze7cLkL37npowLkgClK0Bur7nopmeq9F6yVA98H+dKyRObb/4ushoKKgV0OjsUmpA1ZHFxD0oKlnNG2EmRf5LG7lbeuNboKr3assbUhhjyooV6adZAotNAr+H/Sg2RP5KA5BD74vCS+2j603Rr63XPsvo8HlnmhB/DCvztjzfBEpm4RvvM+Xo/Pa07W5O1IaK1FR3jHt7Aycix64Y9373a6eJMliC1JCjyNLyIleW9Mi5V2T6mhnS6AH+18i98cykfBAcVOkWGNJMtWn/U8/AlZFHdeb0VT8DOQTOgB15O5Gyi+LxEf1AeSe+RjV12o99Bsuga7z01T+OyG5ysj0cJ1ylZWpHrk2Qg+CHVBneF3Cuv0s1BlaiNoZ5+9RbYB538mc8DTwGrpfLvC29wvUFaNHYu73LPJ0TQvF91yMDoiRL6bMgmh2aCzqsL+PfOwTK2cjdFqMDoiRNUanxeqbPHljydNJ7WUb5C70EtUDZai9F64gvK6oOzDefU4s/4e79+Honp0VZOmR+dG57RKxvQ/Z+qUePZluoysajA5F//2/o3v0PrJ/i3r0akjWd3OOeTPjPJZAsyZ3uGN7UMkFlgwqfca69wOopc37fJt71UMbje0PfoT0dw1boZHHfN629d225ActWsxslOMn6AGVNWX2KeVnINoo/rOUaWcBNLreEE2Jpq13d1CdswP3/Q7yKao3Vr4009BovUw9o9DNE2IeNG26TWr7BGQhLdPOP6lYFRJeJuyWl9AbKUB/kDmKbHlDHIdu/HlK7l8SKZMP3f6bSPk/FrAOWsiXcA7VEShASvZh5IKYx4XoftmR6s7oL4FfRbYF6ghmWa1/R+V3i5GrSCYaIFdZmWLl8rkbWdcOpDL7exX6zyWL9/qiGYuEpag8ABPmQ88InxMC5XYD/pDaVq8eybvfE8roGqi95+rRAWXkS5c5lYp7WRH16LQQRToiIS1rPTot1NYo4uRtj06KvRcTWqheP3Aa6jxORlbq/6L/d+heiKGV7OdarKxF5VqoXceRp0dGAtdEbo/VL7H6KN3G2lSnDPile0H2b5EmRq+GZA2RHJN1HidT7cL5XaCNxvYHl6EyAAYqLkxPIGvPma7QFlR+zMSFqSvyOctazGyUY330EGqUS1hHcClSQA9m7B+LHswruO8rIevmXe2styxd0EC3N7KolmUQspq/jhY0DXLbu7q6v0iVn0656F3dkeXu3tT2e6m1ZvnMh+7RtMU2S940ndBU6TVO5tj9A9G08RR0ni3Awmi6NZbxyBUkWeA3guoHQiek4B5AuWN8FqNizFgAWXheRA+NdagsYGtx2/PaSvxQl0dWvmR7L6+N3uh/+2yOXGVlKroGIbnKylSPXJtRCZ86EN27j6AO3IpI99+DLN9XI4veNNThS6y7SyN/ap9lkWuoz3h3bn5n8RNqO6pl9UiZ+72srknfc/XogBj5sspsizrmNyDL60QUkjzGN9unUToiS9Z6dFpeW0XytlcnFemjIo5Brt4DkLvJZWi2KnQvtJdYWcueU54egXj3JcjWL/XoyVAbjyMd2QfdjxtQ0S9ZvwWU06tZspJzTNZ5TKUSmAI0YzmnMS8arAXZlWofz2RNQTLI+Cma1vwW+XIZ7eNWaq1uPs2egdgXDXCSzsYYaq13nVAkhG/RepmZFFvlYuqNkQ8UdeFTZCH8iHyf6Kx6RiDlNQRlUx+DlEESjeFRtJBrSaQwdkcWyhfTFeW00w9dm7S7zQk59YCm+Z+i2gWgSF6fTV27q2bUn7X/HmQJ9dkY+UKXYWs0zfwK1b7AE1En4FuqQ/it4vYPd98noWlm3+p5CnqQPEt1CL2stsahqe3HUYcnYZCrfxLqPB/mtmfJVY9MZeUqK1M91+pyZJGfiAYOG7uyfZEFs82V2w+5/iRcjVydQA/bCWhKP4ngdDiaxfAZgv5fvv/ucGrdV2L1SJn7HcrrGgjfc7E6IEa+ojJfuNdpyLV4L1f+4EBd9eo0nzwdkSdrPTotq60YeRuhk/L0kc9oNID+HPV50lF2WqlE/gndCzG0kv98j5U1q1zoHPL0yALIdSedYyBrO4T1Sz16MquNEei6PgOcHWgfqn8LKKdX82TNOibrPHqhPt0L7pgzMuSdlbTR2BmIdQnPUBlN4B7yY0THDCCOdeWS11fI19Dfll7UFtPO8kj5LO9tG0Ptw3cXNCLfBSmikchamRXjPbbeIvkSuiPL5zD0wP2A7Oy2sQOy3sjy9wv3fRm0DmgmepCORzdR2tqa1049D9uzkUUuy3KYJa/PjaSmHCP2L+1k/Zzq/9F05DpgzLk8TyXKxtbAlVQ6/2uRb+29n9rQ3oPRf8m/J+dBD3mfWD1S5n6vR9dk3XOxOiBGvqIyM6idtTg10BbUr9N88nREnqz16LQifZQlr+kkwyimo/qDCXuhtWrGd4A/k79wNebh0Bcp+OSVZO32txX5tYbaaaXysExeM5H14mvkRwl66B+WOvZ4an2hy9ZbJF8Wo4E/ZuwrU8+D1M6y9aKySPQGsqMWhdrpjs5vx9T2C6gEKfD5PZoWXyGwL0RI3kWR8shKe5+1f2s0Tbls4PW9SHmMOZO9CbvS9KE6wVTCD9D9nfZTvxW5ACSU1SMJefd7K+V0Tcw9F6sDYuTLKvMGmiXyGUk4wmB7dVqRjkjjy1pWp5Vty5fXdJJhFNNR/cGE80gZV2LDbRqN5ynaH6Z1GtXReT5x34sevEXcitbF+FyJFsidSiVaxLzURsv4huxYx7H11ktnwoOQMvREnYi0z/Rn7tUH+TqGFoxlMQNNc2+CrHAJm6Cb3OdcFN1kQ6oXrpaVtxWta7ou47is/V+hjtJUpEwMIyErY/V/0L2d5vvIZz0dtvUiFMkkWeBZVo8k5N3vZXRN7D1XVgfE6KN0mUeonjUBWA4NLOqlXh2Rxpe1jE4r21ZaXtNJhlFMR/UHQfd+ZxRZz/gOsAp6SPp+nr1R2LKhaLr2BPc51srSRpzPWz3tjKF2+r8N+VdugRY0bYfcBs7yyhxM/kM5VG+MfKej6bgB6FqehqyLI0rWcyYKaTkQWUzvQH61S7v9m7k6B6KH40QUHq6bV0dMOzujh+4+aLHquehhuLRX5gLX9kYoU2jy8rNhFskLshK/RG2ElJj9fdBveAvywV7GnfcFFHfoDMOnjWwL/HGpckV6JOZ+r0fXxNxzMTogRr6YMmuiDvNxyGK4I7K+J64DjdBpUKwjYmSN0WkxbRXJazrJMMrTRuP6g1tSWS9jfEcYR7VPWQvhpDttkfW1EfeHqaedMdQ+fNMJll5D1j3fPWEU+ZGmQvXGyNfm2v0S+cuOpjoKQmw91yO/5xnIWnoT1YvhdkKLTr9ELg7nU5scK6Yd0CLTya6uCdT6D4fqmEn1b1okL8iSOhMtEgtRtH8NFKnjI2TFmERt0h7DyKMn6viulbF/YdQZhDg90kbx/T6K8rom5p6L0QEx8sWUAQ2kJqHF1C+hULqJ61hLhrxt3vGN0BGxshbptJi2YuQ1nWQY5Wijcf3BjWuOMprO5mjBWZeigoZhGLMRB1Eb4tMwDMOYQ7COa3N5BU3BvkNOfF3DMIzZjNXQWgeLkmMYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmE0kv8DgjW9Z4uHuYsAAAAASUVORK5CYII=\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{at}}{\\left(t \\right)} = \\frac{3.89793959501171 \\left(1 - \\frac{0.8 e^{\\frac{25 \\operatorname{S_{at}}{\\left(t \\right)}}{9} - 100} + 0.2}{1 + 109.376931067915 e^{- 0.44 t^{2}}}\\right)}{\\left(1 + 148.413159102577 e^{- 0.238095238095238 \\operatorname{S_{vt}}{\\left(t \\right)}}\\right) \\left(83.4293361573075 e^{- 0.14 t^{2} + 0.0127783876495358 e^{0.14 t^{2}}} + 1\\right)}$",
            "text/plain": [
              "                                                            ⎛           25⋅Sₐₜ\n",
              "                                                            ⎜           ──────\n",
              "                                                            ⎜               9 \n",
              "                                                            ⎜      0.8⋅ℯ      \n",
              "                                           3.89793959501171⋅⎜1 - ─────────────\n",
              "                                                            ⎜                 \n",
              "                                                            ⎜                 \n",
              "d                                                           ⎝    1 + 109.37693\n",
              "──(Sₐₜ(t)) = ─────────────────────────────────────────────────────────────────\n",
              "dt                                                             ⎛              \n",
              "                                                               ⎜              \n",
              "             ⎛                      -0.238095238095238⋅Sᵥₜ(t)⎞ ⎜              \n",
              "             ⎝1 + 148.413159102577⋅ℯ                         ⎠⋅⎝83.42933615730\n",
              "\n",
              "(t)              ⎞                              \n",
              "─── - 100        ⎟                              \n",
              "                 ⎟                              \n",
              "          + 0.2  ⎟                              \n",
              "─────────────────⎟                              \n",
              "                2⎟                              \n",
              "         -0.44⋅t ⎟                              \n",
              "1067915⋅ℯ        ⎠                              \n",
              "────────────────────────────────────────────────\n",
              "                                          2    ⎞\n",
              "            2                       0.14⋅t     ⎟\n",
              "    - 0.14⋅t  + 0.0127783876495358⋅ℯ           ⎟\n",
              "75⋅ℯ                                        + 1⎠"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MlnP_lD8wxyy"
      },
      "source": [
        "3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 101
        },
        "id": "XuiCuW1kjZFk",
        "outputId": "c072a1ad-5902-41c0-a237-69f33d18a81b"
      },
      "source": [
        "f_wt = 1 / (1 + exp((-np.log (99)/0.175)*(S_wt(t) - 0.175)))\n",
        "dSlt_dt = S_lt(t).diff(t)\n",
        "LAI = Eq(dSlt_dt, S_lt(t) * (d_tt*theta_alpha*f_wt*(1 - (1/(1+exp(-1* 100 * ((S_at(t)/theta_el) -1)))))* (1/exp(-1 * 100 *(exp(-1 * theta_k * S_lt(t))))) - (1/1+exp(-1 * theta_sr * (W_at/theta_sm - 1) ))))\n",
        "LAI"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4kAAAAxCAYAAAB3X+zQAAAABHNCSVQICAgIfAhkiAAAIABJREFUeJztnXu4XeO1/z/JjiRyEYlLJahcxLW5OIjQYFNUXBJt3dscW4s6gqOnKA1O/CrilKYoSuOwlSJVDT1av2haqfstmrRFEezULS2NU5ckgu7zx/edz5xrrnl5595r77l29vg8z3r2XnO+851jrrXmO8d4x3jHAMMwDMMwjPphcNkCGIZhGEa90atsAQzD6HL0LluAkpkPvAP8rGxBPFmvbAHaSH+gGZgLHBvZ/nngWuBW4DagEXjAbWt0bfoAVwOXAzcBAxP6n+Pa3eDeTwUOqp34hmEY7cb0dKMUzgfGly2EYRhdioOB4WULUTKNwKF0HSPxCGD9dhyfZhQfAjwPvAicUGCfL9OAye7/eQn7pwMHAnsD9wI3AiPdvoOAczP63gi4zMn5EHA60AD8dxtlNQzD6Ai+AuxTthBG9+J7wHllC2EYRpdiDFLcDRmKXcVI7Adc3I7jG6k2insBLwCbAwOQQbiRx74kxgH3xF7rISPvM67NrQnH/QLo6V4An0JeQ5DncDZwM/AFYAKwJ+HE6CHAV4GJwEmRPudnyGkYhtHZ9AYWobFqnaZnfhOjEzgZ2Aa4qGxBDMPoUnyTZGXdqG9WAc/Q9tnoRcB7sW0TXJ+vA+8jT94BHvtGA78EFqMQ0U2Bpchoi74+Al4DtnDHxfWHnd1x/3QvkLezj/v/PWRkfg15HHdE17+L278B8L/AWOAPkX7XJpzLMAyjLNaiCa2bgM1KlqVDsYG3fPYAZlI5c2p0X/ZCs/GvA61AUw2PGYoGtbeANcCzKCwsYCBaL7QcWA08Auwa62M6UuDeda9HUbhjlAbgO8Ar7jyvoAmQaBx/nsw+fbS4Y+OvXxbsZ2ZCHyuo5pRIP4uRFySKz2fjcy7f73MSsAz4pA3HGuVzJzLya8Uw9L0HvI48h1n7+gDXAF9HRt6tZD+Lfg4cCfwQ/c4mIaMPpDTd6P6fCvwIeQ2vcduuAa4ErkNe1P7ASuB6t/9FFDa9wskzKnLef2IYhlE/vAxchcLuG0qWpcOwxZfl0hst0J8NvFmyLEZ9MAD4E/Bj96rVMRsCD6O1PgcjQ3Ek8LdIm+vRLP5xyGPwFWAhsAOhgvka8C2k0PV0be9CCmYw+/8tZDAdB/zR9XkT8CEy2Hxk9uljVyoH56HIePtpwX5A4XeNkfdRwwvgKOAKZCg+5P7eiz6bv7g2Pp+Nz7l8fwNfA37QxmON8lmDfjO7owmFMjgMefTuce/7oMQ0aXyAjMEoD7m/0yPb7navKKfE3u+AjL/PorFpMYqqmYMMUIAt0f1kGIZRb1yDJmLPAi4pVxRjXeR85Jno7pkJjWTep7gnKO2Yi5Eilsb6wMfIAxBlMflh0CvRzH/APYTrkAJuIlRE4yTJXLQPgBkoXC2aEMSnn5nIsMricZTRMcqLaIIni/hn43OuKGnfZw9knGZN9LXl99OVaaTrrEkMOA6tR4+zOTLy/45+03ei9X1RGqm83j2oXL93OWEG0rR9FwHHtE30DqGRMDwVFIq6STmiGIZh5PI5NHn26bIF6Qgs3LQ8NkXrMy5D8c2G0ZEchgydech7uAQ4FRkbIGOjAXk3oqxGIWVJNABHI+/VI5HtD6G1Rtu59zsA+wK/KiBv0T56IM/aLU7mov2MBN5Akza3E2ZkBE3i7AzcFzvmPqR8J5H22eSdy5ftUFjwx204dl1kIXAHyqAZeOe6Ak+iEOEoI4Cnkfd+EjKcNkblJLJ4AiWVCZLTTAYW5OxbgcpXBIxt22XUjEXIyx/wFIp6MAzDqEd+g6KUkib7DKPNXIxmiAeULYhRt9TSk7jGvWYDOwHHu7anRto8AjyIFMkGFG76CQqPjDLGHfsx+g3H1931AGahULKP0Nq4LG9kksxF+zjAtRnXhn4mo3VWY4H9kKK6gjD74zB3XFyZv4Din03eueKkfZ9fojKstsixRv3QG81CR1lAdebT/dA614CFyHhaRaVRPAVlMV1G9drCpH39UUj0n1HSme+28ToMwzC6K4chHWPHsgUx1g2CLG5XlS2IUdfU0khcS7VH62Lgucj7UcDvkEH0MfI+3BJrA1Jst0betdnA24Rp8UEetFfd36BEw0rCBBc+Mhft4w4nb5yi/YAmbv4G/Id7X8RIzPts8s4VJ+37/HeUGCQLn9/PRSQn/4m+GnP6MNrHasJJgq3QZ74KfX/BazUKPTUMw6g1W6IJy2fR+vkjSpWm69EL+CvSlwyj3ZyEKV9GPrU0EpcTZhEMmEa1FwPkXRjq/p9HZbbQJBZSWfD6VWTERDkPeTCSSJK5SB+bIiP4xIR9RWUJuB9lcAQZfh9T/eC8GhnVWcQ/m7xzxUn7PmeQ7/Xx+f1sjEJXs179cvow2scbyDgEefv+gSYa4q91cs2LYRilM5SwXulmKNS9f3nidEnmID1haF7DrkTR7KYno5TdoztAlu7EMShU6MGyBTG6DQ8D28a2bYOMxzgfuNdgtF7p7Jy+e1KZbKIf1Rk7P6HYGugifTShdUy3tbOfgL7IOLrfvV+LEvjsjzyWAfujhCJZxD+bvHMVoRZryt92ryK01uC83Z0ekf97EZZ4+AgpZyuQkW8YhtHRvEmYYX8FeiYMIXkS2UjmDuAbSL+fU7IspXEtlUqSUZxhSEm9uWxBjLpkAJrRG49Czi5w/0e9CKeiNURFjtkVKaAzkFfiCOSxiKat/zxaMzcCGUBLgMeA9SJtLkH1AYej8M3ZSMGdHGnTjNZJHezafQFNikQXdufJ7NMHSNl+gerMo0VkuQzVixwB7IYyn75L6N0BlcBYC5wAbI/KYbwfa+Pz2ficy+f7PI1qz7DvsYYYXLYAjg+BQe7/wej3OR+tHR6F7sWrsURzhlGP+NamzauzWwvORcmw3kXjyP+QvNzhUsKkVnF2Jj0D97VoqVRefeLuSAP6bBaXLUiZPAZ8u2whujhfQzfU9LyGRrekkeQBuDnSZiaV3hyfY0CG0lL0kHoBOJ1Kj8aRwEtIaX0TrZkdFOujGXkfP0Rr6RZSmR0RYCBKsb8craV6Ga1/7FtAZp8+QJlLW4EJJOPTz+0o5G8tetDfibKgxjkFaHHXvpjqNYrN5H82PudqJP/7PJTkcg8+x3Ykw1Ht19vd+/7u3HNRyYX4ex8agQeQgtKY0kcfZEhdjkqcDEzpaw6hZ/cG93cqyooKClmejrzS1yNDrSPphxSLKLsAv3Xb30P37LkdLIdhGG3jIPRMORxNzDUltDkKTdKeiCYZf4AmGWs9ebcAJaX7DJqonI88g0Ni7X5HZZ3ggCHAMyRn7e6Bnl1HoJDU4LUTmgw9rv3id3l+jp633WJSdjwKgVqN0rtOQK7ng7IOMnJpRj+iXUqWwzCMrstwitVb7GwCI3EaoSd1XsJ7H/YG7gVuROVCkvo4iHxDaiPkyQU4BJVHOR3NAAfrRq9ACtxQZIy2NeJjPvAO+XUbt0cGsGEYXZ+0deBtrbPbXgagyLVD3fveaIIyOoH4rNvXB41F01L6moCSZ8WXqSXVJ+6ufAt9pl8pW5BakRa+MhrNNDyOZiPOQenW+6EQtDK5Cc3SF1lUuzP64k7oEImKsSeaUVpatiCGYXRZWtBDud5L6GyBkgeBlJX4+4BxKPQ2+grCnB9ERuE5wH+m9PEgyhp9MwopjrI9mvTcnVAhehsVq7/S9TGEUIG6yp3nHNI/3yaykwJdAfxrxv6A3clPfmQYRtelLXV2a8VApOe/495/TFguZzc0GfZZ5CVsRhEMaRNjh6GQ0mht3rT6xN2VQK+PRxl1NkXtpMI20gLg1ti2uSjFqw+N7vgWFNr2Lpo1uQst7Gzr2opdkVs7LV38N9CFJoUxzUchdGUqVRsi+fIyKxqGYeTxX1SHs3YWo5HCsBjNPm8a2x/1JB4Y2RZ/X4TeHn30RmG+I1B48LEom+0J7v8vunYnARMjx81Dn+WhkW2bk551ton8zLGN5HsS59LxIa2GYXQOSZ7EIiWUas1Pgd+jaImAQ5BOHl1qMgnp1ksirzGxvp4hHD8D0uoTdxaHo8iPB9E1tdK+MhRboGUIb6BlIy1oCYPv+vXNnAw+zrRG6stO8raRtnQd7Brbfg3pC10DGlDtrla0lmIeStN+GfAr9EG8lidABveR7da+xZ07nsUR5Cpvpdw1lbs4GRaWKINhGOsGQ8kvr9ER9AF+jR6ooKzX57n/N0RrB5cBZ6KZzBuQsXVswnsfpqLnyjykaCX1cQ3yCt4I7IuKzx+PHpSnuja7Ej44p7i2o9z7eSjxUD/X7lrgJ6SvLWmi/UZiL6QQGIaxblALI7FWtWvnIGNnZGz7+RTPrL818hTGPVNp9Yk7iyWE9sZztM9IHIUcYa1oXL4EeVZbUaLAjdIPrWCNkyeNerWTvG2kKcid3Du2/TE0c53FBe4kd1Od8AIU0rNfngApbIOs46wC0s+hD71Hxv7llJcl7ij0+aRlYjQMwyjCd4BNOvmcRyHlI5hxfg6txagnzgb+DaUjPwWFVPUk2ajeEilmV+X02Zvwmv/iXsH7+PMS8o3EI7E1/oaxLpFkJBats1uL2rXfR16h7RL23Ykm1IpwJloCECWrPnFnsQ+KaulBmLStrUbiAnf8abHtc9z2az37edm1j0fXBNSzneRlIx2KLiCaHW5Pt+3ojON6oHUercjlWmsucX1/LmNf0iu6CPc/3bayQrTOdudPyiplGIZRlEF0fubLi5Dx1RVppLpu5S4UN7SbaJ8nsTd6HhmGUZ98CSXMehsZQy8iL0tDxjFZiWviivsLdEzimitQRtPtU/Yvo3h+jgcTjjkbGRv1si6+kbYbiaPcsa9QbSANRN/rB/it8XuQ9Izr9W4nVdlI8SxFAE+hWNzLkAt0OxTKA9lxthsQumM/yr2U4uyHEgw8lrDvabRQ8zjgERQKFbAo8v/D7u/+5IfOdgTBrMGqEs5tGMa6xz/QzPCOaM1IZ7ACPURuc+/HAn/opHO3l0UJ257qbCHQuqB4zU/DMMqnARkaRyOD6g6kE08GZqEwvWi5hwEoHBNkYHwaJcpaiaINQN6om1Fo5sMoRH8Y/t4pX65GCv9hKFlNYIi8714gvX87d/5VVJfgibMJWr99eGRbD2Q03h7ptyuzj/t7H/LERXkPfWcHoM/hNzl9BaGmGyTsq3c7ydtGOoawrtgjwIXIis4L03wVWaFPo4xHW2Q396Y/ctf/MaPNSe7cJ2W0GeTa5MVQn4Fq0fm+DsvpL+Byd/7TPdsbhmHUG/3Rmo0/o2xu3y1XnFJoItuTuBAVs16F1pfsntHWMIz64Sqkp82m0pGyHlKiW6msbduIX23avDq7tSDNUzQz0ubLaEz6J+mJuaJ8FdkBUfLqE5dBI233JF7qjv1myv7gN/FvHn3d6dpOTdlfz3aSr43UZvZAMy/RH+dyNFuSlsHtEiot2iS2cX3FUwhHuRa/+oOr0Ux4Fi3kLxxuS6HqudRPKQ7DMAzDMAxD7IaMp7SEUoGSfXynSVQ+d6PQ0nqnkbYbiUEimTTdfJbb77O0I0gMk5aYrd7tpAobKSnctD08ggSdhMKR9kY33dfRzXUy1XHZ46kMY70UhS9F1w0G7tl3SOdfkPs2y4oGhQB8KqfN8Jz9baW1g/o1DMMwDMPoTrQAWxVo/xOyC52fhkIpV1HpfQv4jPtbVvLDMniYcGlBe2ihtt9VvRL8NtL0/Xq3kypspFobiaBZmAfcC5Sp53IUJ30poTctYDwqahwwIXJsQFCks2/KOXuhmi7PIld+FutTXtHPD9zftOswDMMwDMMw8nkJlQzw5Y2c/Qe4v3mJuZYXOGdXp1bLCWr9XdWSf7i/SdlGo9vz1m9CmHn2g4w29WwnVdhIHWEkxlkJzEAXvwH6MP7u9m2GLNYghfj7KO57L1R36zkU+/031z6tTskO6IN5OkeWnqiO1ys57c5w7XxZgl+9q+BHk1a/xDAMwzAMw8gnKYtjW+mLkrQ8gLw7Rm2p5XdVa4J6lduk7B/t/r7g0VdgJBZJ6FMvdlKVjRQYie0Ng0yrSxgw1P1d6V4B45HF+ryTYXeUaW43lBUqsHbfREkA4sUfo/0A/D5Hjm2drFlZWkFGYhG3+E34GYnBLISPAWqhqYZhGIZhdHfydMxanmPjTjiXUV/c7/4egAylaIbTgajO7iqSs4bGCcpk/COzVTX1YCdV2UiBkdjeG/AraKHjb6g2bkYSxtdeTrUL9Y8oZSvoQ3oPeDLWrhXN7nwJpRpeFjtHYDm/myPnRPf3/sxWHbcmMbDOh3m07YxB0TAMwzAMo7uzGpXyGQt8Efh5QptJwKOEOqvRtRiFvHAvUVmC4iWU8OUAYDrwg8i+C5Hhdx3ZIaQBgX4fj1jsCnaSr41UwcmoiGgW9xNm6LkZuBi4Evj/KCVrK6rfEi9Cejv64APOR4UokzjG9TM9Yd9ebt9rKJ53JnBEQrvbnDxb5lxPRzEOyVlGjUbD6G70IUw0YBiGYSQz2P39Iir9UEZo4L+UcM44ByDjoRVlk/we8H3gp8iQ+Ev6oUYJHIaqCzQje6MVfU/Btsti7Vtcm+EJfY0C/ur234Xug9+698+THsYZpReyMZKSx3QFO6lNNtK1qJgoruMkA2c34DtI8OVoceoqFL97A+k1ov5MZd2RO9GHlkRv9AU+nrL/VPRFrkEfxKzY/kFopsgnLLSjGIDc2HEL3zCM2nMGmjU0jHWNySi5wTzqe62P0Tn0R0rxXCpT7w9HOtjtsfZ9kS51oHt/Q2TfMODEjhAyh2OAzUs4b5xdgZ8hr89HwNvIk3Mddq/VGzPJLk/XEmvfQrqRCDKObkShm2uRPXM54SRKHsNd/08m7Kt3O6nNNtJjwLfd/79DF1kL+iH36cTItmVk1xA8F11YWi2RLE5zx05qw7G15A/IUOyf19BoF1sCi1Ampz9QOWMyAs3qPIsG//h3kXVsi9u2hNAlv617H7xWoxkugG8Az7i+rkRhxGn9p/WT1T/AfDRz9bPYdSTJCnAIGihepPJ+S2sf0A8NbtHZuaTrw13jfBQ7v4xKJSSNAagIedDHSGCK+38w8EuPPgLGokK1htGZpN1bcdLuWUi+z6L3QpTBVM4yF8FX1rR2SddQ67EtaXzZEI0rS4A/UWnQJLXPO0fW8yDpuzjTneNPVKbobyF5/MySN+2YtHE1jWlo4gA0cRAnbiTOAM5BRuIhwEPA6WhS7TtI2exs+gD/VcJ5DaNW7EfoEawFnWknedlI49FAtRoNlhNQDO4UZFVHLfRnCwoQZyK6+H6RbS1oMB5GcnKXvmjA/p+C51ofpdNNeiB3Nlehz2+3sgVZxxlKuFB3M+B1wof/74A93f9DqM7ym3VsCzJm0hiAZh77o0xpL6HfbQOqN7R7Tv9J/eRtbwQOJdlIjMvaC81cbe72RcMo8q5tFlJAAoUp7fpw/wc1fHqgzFp5nIHqBAVMR4pMwI9In22L82OKZSg2jPaSdW/FaST5noXq+wyq74WA75KuDDS5V3tkzWqXdA21HNvSxpcGQr2hP1r7s1FG+7xzZz0P4t/FGJQdsC/SKx4jHGdaSB4/0+RNO8bnOuKcSxhaf2vC/qiROBE4Dv02DnTvg3F3NnCRx/k6iuvIr2NtGPVKYKAdXaP+OstOSrWRogVBR6PB8nE0EJ6D4rD7oVmwYNDYDT0IPltAgCTGo5nJVZFtM9CH+xoarOKsQTNmT1HMEzccKZhntkXQGrPI/fX9/AYj9/GoDpFm3eVNwgxNK5BiMATYEYWQBDHdK1EMts+xPkxBC5ODBc690E27nnv9zbP/eD9Z2xehhcw+TEAz1K+jVMr3EtaGymI0sJ1rHyXp+vqikJ2HXRvfSaVjgbvd/3ujGe2voWxc/YFfUFm/6g7gmwn9NKCF2z41jQyjVhS5txaRfM8m3WdJ9wJu26/Jz+rdHlmz2iVdQ63HtqTx5RNCvaEPmoTqkdE+6xxZz4Ok72J7lLhkDZpMX0oYsplGlrxppF3HaBRRsRglqdjUbX8N2ML9n1fofV80sXAs8mqORd5MkJJ7HrrGMlhC/udpGPVK4PxJWzNYlM6yk4bjYSMtoHoGai4yUEAhCe9iWTfbywD0gPqFZ/tLUYx0wF7u2NeR8t1US+EiDESx2MvRw/ARpPgXbZPGKWhGdQ164O2Z3bxd7IzCfEBhRnehWZanCUOpfY4FybwYxZx/OaH9XWjxf8Bp6L5ZiRYq5/Wf1k/e9kaqZ4GSZD0cebMDziIcGLKu7W5UQ6iJSg9H2vUtQoPYlYSehSz6UF2geBGVaweGoYEvYIw7b7wA7jgUChelASnVwW/uFTRjHvUaTEfK0rvu9ShwsIfsAcEs4lUJ2590fb6FfnvxhDo+95KPfL7XMBSV7nkLfR7PUlkbzGecmUn1GpAVbl9Lwr5WKkOGfWXNGyt8zpUla63IureSaKT6nk27zxZReS98FSnU11LpfY/SRPrzwVfWvHaNpEfo1GJsSxtfNkQG2ioqkzTkjbfxc2Q9D5K+ix2Q0bwhmsB9nnCiKmv8TJM37Zik6+iDJgUCY/BkZNCBlMEbgB8i428SmlTYEP1GllH9/TYhg2wK0jE6ciLaV2/ZG7+lCYZRj7xBfr32LsmW6MaNKyXXECaqycqoYxTjJ2gGdv2cdv3Qmo9ojPBB6KFxOHrgNBU8dzNSmPKYh4p0NiKvzExU92Xzgm2SOArN3p6IZmZ/gGapP+0hV5RgjUf8FS0xMgQ91Pdw7w9HRUq3RA/d+4H9U/qPHwvhtQ11+8ZG9m1A6EkDKRELXD/rI0Vvr5z+k/rJ2w7JylqSrFlKX9q1TUWTFVCpMGVdX09gH3euVaSHxAULwodRXb/05dj79ZCSEeUpqjN5TaZa0fg2UrgORcr2FHRvnR9pM9UduzVSDmeh32n0O05jIlL4llJtJC4AjkeG4RhkwK6g0sPicy/5yOfTZkP02f4YeYpGoIQM20fa+IwzM9Gi+s0ir03cvk1i23dCa7GPKyirz1jhc64sWYuQNea010hMu8+g+l5Iozfh2ru/uFfwPrrOrKONxFqMbXnjJyg08WH3N6990jnSngdZ38XXkSJ4P5poOcNtz3o2JMmbdkzadRyFlNDg+3wO+FbCOTqTZvz0CV+9ZRzK9mgYXY2dkR1VDxGLNWcKCrGIL1Z+jHAhcVZGHaMYB6Af05dy2h2OFNs07+37dIyRuD76PUyNbV+MvC++bdJ4HHmpo7xIpet8c6TE/h2FDd5J8bUKfVBIzrTItt2pzNB7lnv5HBvnUio//2nALZH3R1C5gPks4GyP/uP95G2H7Bn9qKx7UOllu5zKbHjx9qDv5VXksXkbGS8XkH19Ue4l2esKoTE3BCnxAVugZApRBlKdGfiChHbHUlnnCOAepNBFucltz2IlUgqzGITWEO2DFLq4kRhnAApBO9S9b8+95CNfvM3FhKHAPqSNMzNJ9hQlMQPdx3kTY3FZfcYKn3PNxE/W9ow7vvdWQCOV92zafZZ0L/jQRPrzwVfWvHaNVI87tRrbfMeXa9CzMq990jnSngdp30Wc60n2fsefDUnyph2Tdh0XURluXw8042ckRsnSW0YBT7RdHMMojVlocrKsEnsdQhC73orCsfpE9u2J4muD9Q7jCOPWjfbxa5QY6F9z2u2JFMV44c2Ophf6PayJbV9N6NX0aZNEbzTjcl9s+32Es84j0Ezt666vRmBjFDbjSw/0APstqkkT8CRaxzEY/f73QjOyPsf2R4YKSNHfF83+BhxJZWa5V901BQkIGlF4Ulr/af3kbU8iTdYnkEcrSEQxGSlJWdd2Lhr4hqNZsrnA/8u4vs8Tlp4Ygdb1BEbJhciAOxOFsG+DsuqtREp9EP65FVrfFGVrqr+rJ5A3LGoQJHnpH0JG3Hbu/Q7uGn9FMg0o7n8ACv3M4kdIUfYtQDsQ/faCWkptuZd85EtrcxgyvuYhz8oSlBq7LUsJRiLvxisoOcbIhDY9UOjbLeiafGX1GSuKnCtP1vaOO2n3li9p91nSvdBefGUtek21HNvSxpdPEY5Vg9AY/nxG+6xzpD0P0r4LCNcBbovGnrzxM03etGPSrmMFYTIw8Itw6Gr0Qwa5YXQ1DkeTzq+WLUhHMBQpKNehmZyD0dqYVkKlqoXsjDpGMY5B3oThGW3uotr7EaWjPIkgRe1BpBw0oFTfn1D50PVpE2cY+l3Fw4YuiBy3gOr1JPuhNRq+TEKzOtHU52PcvsnISP8TMCdyzJKcY0eicMKl7th/jxw7CK3fjXvjZyGl4xnCVOZZsqX1k7YdVDbiLRTG8xqaHc+SdQrKWLiMcD1TVvsoTVSGXiVd3/XIs7YEGYf7ubZbuPYXAj+nMqseyIMTJHQahCZI/kiYGfUMtD4tylj0e4qup5mAkm5F6UE40xcUS07y0o1B99XHyJOUtybxRCdnYBQvIt+T+FM0+RYtmut7L/nIl9dmjXvNRqGZx7v2p6bImzbOTEaK91j0HS9Cimw8S2YQOTGuoKw+Y0WctHP5yFqLcSfp3gqIhlMn3bNRmgjvs6R7wYcmsp8PvrKmtUu6hlqPbUnjywTX71I0cf31nPZ550h7HgQ0UTnmPYrW8D6JJjEge/xMkzfrmKTr6I90gj+7Y76bIGtn00xtPYmfJT1axjDqlc+h507a5OU6wTFUJk24ECVYCbyNX0YPgn+ixdFG+2hAD6YrMtosILsGlo+R+G3XLnh9hMqZRLclJY0ZhbLdtiIF7gk0eD9XsE2cPMVvK7d/VUzG1SgEzOi6XI9mzMcB30MKZ7T+z0SyvTa/obqo7Wj0e4kmglmf6ux8R6MZvqOR0joNeS/jtRR7I4/lzsiIepvqJDMB2yIledvItkVkG4lzkDcr7sXyvZd85Mtrs5Zq7+PFCecK8J2MGoA8k/8R234H6SFkWbK2xUjMOleWrDbuGEY+bdUnomSue3RCAAADz0lEQVSNJ8dTvcbcMOqd+SjE3jBqyl5ICUlL9PITqj0iUXyUtyFICQtewdrS6LasdUL9kacZFKqTVNDcp01Ab6QEHxHbfjVSkqegcJOtE15FE9sY9cVZSMGfi5KKJGXV+yrJYY+DqSyAHbAbUu7j68buojJBxatUe0fPo3qNY5yFwH+n7GsiNOqCVyuaSPuYyvB9gO+jsMHtSKfIvZQnX1qb5chgjzKN6pIEAUUiFu6nchJxU6REnpjcvIqorHljRZyi54rKauOOYeTTXn0CsseTK0kOWTeMemUMmizZpWxBOoJ4EXGjc3kArY2ZRfKg+fuU7UVY6V4B77n3ecpxwAfuNRith0hKHODTJmAtCp3aH836B+yPHjgfIUV5BXqYGOsOlyZsi5eCSUt//g4y/OJ8Bq0h+2ts+w/RmscgqUY/FL4Z5RPya4r1pNrYC7iLypIcIKP3ReSZWxvZfgXKTrgPlQl64hS5l/LkS2vzMJXeT9Da0HgJkqL0RQZwdG1mE/AhcJtnH1FZ88aKOEXOFZfVxh3DyKe9+kQWPd3LN5OvYdQDs1FegrguYBg1YQMUOhUPqQLNUHxC5bqZAaju3HgUGnWB+993trsZvzUEn0drNUYgpWwJyna7XsE2p1KtFB+FFMATUFr7K5BithVSjt9C7vudkJdpf+Q9yFPoje5HM+metBmxdq+hNW/DgS+g39n3Im0uQaFSw9G9Nxt5BSdH2iT9nqMsojrc9Gq0rm1fKkswDIi08bmXfOTzabMrMopmoJn/I5AXLRrm5TPOXIbqmo1AHt173HVu5fb3QGvZ4tlJi8iaNVZEyTtXnqw27hhGcZrx0yd8xpNDCNevGkZX4GA0KRyv1WwYNWUsMhSHJOx7lErlrZHkwtHNnudqxm9QPxIlH/kQhchdRfWN4NNmJsnZWU9ByZA+RN6CqJG8C8qO979opnIpyjZnGFH6IuNmYsr+jQnrM8aL1b+MvH3RkNRmt/9DtF5tIZXZBCH99xywiGojMel+baXyPvS5l3zk82kDergtRQlsXkAZZqNhvo0pMjdH2tyO1leuRd7cO6lMrLKPO2ZCwvmLyJo1VvieK09WsHHHMIrSjJ8+0Uj+eLJf1VGGUb8MRhPGO5YtiNE9mIoyPsY5EBmQDQn7DKM7M53q8giGYRiGYRgdxXooGuWgsgXpaMzwqB+eRzNrA9BMd8AyFO70JlY/yDCi7ITWHlr2ScMwDMMwOoMj0QT1r8sWxOh+tKWgtWEYhmEYhmEYHYvp6YZhGIZhGIZhGIZhGIZhGIZhGIZhdGP+D+JYrc1GQKQSAAAAAElFTkSuQmCC\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{lt}}{\\left(t \\right)} = \\left(\\frac{1.16938187850351 \\left(1 - \\frac{1}{e^{100 - \\frac{50 \\operatorname{S_{at}}{\\left(t \\right)}}{9}} + 1}\\right) e^{100 e^{- 0.75 \\operatorname{S_{lt}}{\\left(t \\right)}}}}{\\left(1 + 99.0 e^{- 26.2578277150548 \\operatorname{S_{at}}{\\left(t \\right)}}\\right) \\left(83.4293361573075 e^{- 0.14 t^{2} + 0.0127783876495358 e^{0.14 t^{2}}} + 1\\right)} - e^{10 - \\frac{2 t^{2}}{7}} - 1.0\\right) \\operatorname{S_{lt}}{\\left(t \\right)}$",
            "text/plain": [
              "             ⎛                                                                \n",
              "             ⎜                                    ⎛             1          ⎞  \n",
              "             ⎜                   1.16938187850351⋅⎜1 - ────────────────────⎟⋅ℯ\n",
              "             ⎜                                    ⎜           50⋅Sₐₜ(t)    ⎟  \n",
              "             ⎜                                    ⎜     100 - ─────────    ⎟  \n",
              "             ⎜                                    ⎜               9        ⎟  \n",
              "d            ⎜                                    ⎝    ℯ                + 1⎠  \n",
              "──(Sₗₜ(t)) = ⎜────────────────────────────────────────────────────────────────\n",
              "dt           ⎜                                     ⎛                          \n",
              "             ⎜                                     ⎜                          \n",
              "             ⎜⎛          -26.2578277150548⋅Sₐₜ(t)⎞ ⎜                  - 0.14⋅t\n",
              "             ⎝⎝1 + 99.0⋅ℯ                        ⎠⋅⎝83.4293361573075⋅ℯ        \n",
              "\n",
              "     -0.75⋅Sₗₜ(t)                                      ⎞       \n",
              "100⋅ℯ                                                  ⎟       \n",
              "                                                       ⎟       \n",
              "                                                2      ⎟       \n",
              "                                             2⋅t       ⎟       \n",
              "                                        10 - ────      ⎟       \n",
              "                                              7        ⎟       \n",
              "──────────────────────────────────── - ℯ          - 1.0⎟⋅Sₗₜ(t)\n",
              "                              2    ⎞                   ⎟       \n",
              "2                       0.14⋅t     ⎟                   ⎟       \n",
              "  + 0.0127783876495358⋅ℯ           ⎟                   ⎟       \n",
              "                                + 1⎠                   ⎠       "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HjrFJvh_wzCx"
      },
      "source": [
        "4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "id": "-lRW_rmpw0JS",
        "outputId": "a72a4f69-a4da-4119-83f6-49306ea11328"
      },
      "source": [
        "dSbt_dt = S_bt(t).diff(t)\n",
        "BIO = Eq(dSbt_dt, theta_rue * W_st * (1- exp(-1*theta_k * S_lt(t)) * f_wt* d_tt * (1- (1/ (1+exp(-100 * (S_at(t)/theta_m -1)*(1-(1/1+exp(-100*((1000 * S_yt(t)) /(theta_gx *S_gt(t)) -1)))) )) ) )))\n",
        "BIO"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{bt}}{\\left(t \\right)} = 1.15 t^{2} \\left(- \\frac{3.89793959501171 \\left(1 - \\frac{1}{1 + e^{- \\left(100 - \\frac{5 \\operatorname{S_{at}}{\\left(t \\right)}}{3}\\right) e^{100 - \\frac{20000 \\operatorname{S_{yt}}{\\left(t \\right)}}{9 \\operatorname{S_{gt}}{\\left(t \\right)}}}}}\\right) e^{- 0.75 \\operatorname{S_{lt}}{\\left(t \\right)}}}{\\left(1 + 99.0 e^{- 26.2578277150548 \\operatorname{S_{at}}{\\left(t \\right)}}\\right) \\left(83.4293361573075 e^{- 0.14 t^{2} + 0.0127783876495358 e^{0.14 t^{2}}} + 1\\right)} + 1\\right)$",
            "text/plain": [
              "                      ⎛                             ⎛                         \n",
              "                      ⎜            3.89793959501171⋅⎜1 - ─────────────────────\n",
              "                      ⎜                             ⎜                         \n",
              "                      ⎜                             ⎜                         \n",
              "                      ⎜                             ⎜          ⎛      5⋅Sₐₜ(t)\n",
              "                      ⎜                             ⎜         -⎜100 - ────────\n",
              "                      ⎜                             ⎜          ⎝         3    \n",
              "d                   2 ⎜                             ⎝    1 + ℯ                \n",
              "──(S_bt(t)) = 1.15⋅t ⋅⎜- ─────────────────────────────────────────────────────\n",
              "dt                    ⎜                                       ⎛               \n",
              "                      ⎜                                       ⎜               \n",
              "                      ⎜  ⎛          -26.2578277150548⋅Sₐₜ(t)⎞ ⎜               \n",
              "                      ⎝  ⎝1 + 99.0⋅ℯ                        ⎠⋅⎝83.429336157307\n",
              "\n",
              "1                     ⎞  -0.75⋅Sₗₜ(t)              ⎞\n",
              "──────────────────────⎟⋅ℯ                          ⎟\n",
              "         20000⋅S_yt(t)⎟                            ⎟\n",
              "   100 - ─────────────⎟                            ⎟\n",
              "⎞          9⋅S_gt(t)  ⎟                            ⎟\n",
              "⎟⋅ℯ                   ⎟                            ⎟\n",
              "⎠                     ⎟                            ⎟\n",
              "                      ⎠                            ⎟\n",
              "─────────────────────────────────────────────── + 1⎟\n",
              "                                         2    ⎞    ⎟\n",
              "           2                       0.14⋅t     ⎟    ⎟\n",
              "   - 0.14⋅t  + 0.0127783876495358⋅ℯ           ⎟    ⎟\n",
              "5⋅ℯ                                        + 1⎠    ⎠"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9T0KKlM7x-71"
      },
      "source": [
        "5"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "id": "SXa54c1SyBg9",
        "outputId": "39077850-4db0-49e0-e384-c78d2b85ea6a"
      },
      "source": [
        "dSgt_dt = S_gt(t).diff(t)\n",
        "GN = Eq(dSgt_dt, dSbt_dt * theta_gb * (1 / (1 + exp(-1 * 100 * (S_at(t)/theta_a)-1))) * (1 - (1/(1+exp(-1 * 100 * (S_at(t)/theta_ts -1))))))\n",
        "GN"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{gt}}{\\left(t \\right)} = \\frac{20 \\left(1 - \\frac{1}{e^{100 - \\frac{20 \\operatorname{S_{at}}{\\left(t \\right)}}{3}} + 1}\\right) \\frac{d}{d t} \\operatorname{S_{bt}}{\\left(t \\right)}}{e^{- \\frac{25 \\operatorname{S_{at}}{\\left(t \\right)}}{9} - 1} + 1}$",
            "text/plain": [
              "                 ⎛             1          ⎞ d          \n",
              "              20⋅⎜1 - ────────────────────⎟⋅──(S_bt(t))\n",
              "                 ⎜           20⋅Sₐₜ(t)    ⎟ dt         \n",
              "                 ⎜     100 - ─────────    ⎟            \n",
              "                 ⎜               3        ⎟            \n",
              "d                ⎝    ℯ                + 1⎠            \n",
              "──(S_gt(t)) = ─────────────────────────────────────────\n",
              "dt                          25⋅Sₐₜ(t)                  \n",
              "                          - ───────── - 1              \n",
              "                                9                      \n",
              "                         ℯ                + 1          "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aSObdQdhziFO"
      },
      "source": [
        "6"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 62
        },
        "id": "rjSCB1Fly8Me",
        "outputId": "e7a5515b-b672-4bae-d2a7-7f5e1180d025"
      },
      "source": [
        "\n",
        "dSyt_dt = S_yt(t).diff(t)\n",
        "Y = Eq(dSyt_dt, dSbt_dt * (1/ (1+exp(-1 * 100* (S_at(t)/theta_a -1)))))\n",
        "Y"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{yt}}{\\left(t \\right)} = \\frac{\\frac{d}{d t} \\operatorname{S_{bt}}{\\left(t \\right)}}{e^{100 - \\frac{25 \\operatorname{S_{at}}{\\left(t \\right)}}{9}} + 1}$",
            "text/plain": [
              "                  d               \n",
              "                  ──(S_bt(t))     \n",
              "d                 dt              \n",
              "──(S_yt(t)) = ────────────────────\n",
              "dt                   25⋅Sₐₜ(t)    \n",
              "               100 - ─────────    \n",
              "                         9        \n",
              "              ℯ                + 1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3YVlh9lOzjF_"
      },
      "source": [
        "7"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 190
        },
        "id": "ud-3zeOqzkSt",
        "outputId": "bfbf58bd-4095-44ef-ff9b-e2c6c4e7dc25"
      },
      "source": [
        "D_t = (4098 * 0.6108 * exp((17.27 * W_at)/W_at+237.3))/(W_at + 237.3)**2\n",
        "e_st = 0.6108 * (exp((17.27 * W_xt)/(W_xt + 237.3)) + exp((17.27 * W_nt)/W_nt +237.3)) /2 \n",
        "e_at = e_st * W_ht * 0.01\n",
        "gamma_t = 0.665 * 10**-3 * W_pt2\n",
        "e0_t = ((0.408 * D_t * (W_st)) + (gamma_t * (900/(W_at + 273) * W_wt* (e_st - e_at))))/(D_t + gamma_t * (1+ 0.34 * W_wt))\n",
        "#k_ct = k_i + (1-exp(-1 * theta_k * S_lt(t))) * (k_m - k_i + (k_i-k_e)/(exp(-1 * 100 * (S_at(t)/theta_a - 1) ) +1) ) - ( (k_i - k_e) / exp(-1 * 100 * (S_at(t)/theta_a -1) +1))\n",
        "k_ct = 0.45 + (1-exp(-1 * theta_k * S_lt(t))) * (1.3 - 0.45 + (0.45-0.2)/(exp(-1 * 100 * (S_at(t)/theta_a - 1) ) +1) ) - ( (0.45 - 0.2) / exp(-1 * 100 * (S_at(t)/theta_a -1) +1))\n",
        "e_ct = e0_t * k_ct\n",
        "dSWt_dt = S_wt(t).diff(t)\n",
        "SW = Eq(dSWt_dt, ((W_rt)/exp(-1 * 100 * (S_wt(t)/S_xl + 1) ) + 1) - (e_ct * f_wt))\n",
        "SW"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} \\operatorname{S_{at}}{\\left(t \\right)} = t^{2} e^{\\frac{2 \\operatorname{S_{at}}{\\left(t \\right)}}{3} + 100} + 1 - \\frac{\\left(\\frac{0.5985 t^{4} \\left(- 0.01 t^{2} \\left(0.3054 e^{\\frac{17.27 t^{2}}{t^{2} + 237.3}} + 1.10462607546493 \\cdot 10^{110}\\right) + 0.3054 e^{\\frac{17.27 t^{2}}{t^{2} + 237.3}} + 1.10462607546493 \\cdot 10^{110}\\right)}{t^{2} + 273} + \\frac{6.55966902608748 \\cdot 10^{108} t^{2}}{\\left(0.00421407501053519 t^{2} + 1\\right)^{2}}\\right) \\left(\\left(0.85 + \\frac{0.25}{e^{100 - \\frac{25 \\operatorname{S_{at}}{\\left(t \\right)}}{9}} + 1}\\right) \\left(1 - e^{- 0.75 \\operatorname{S_{lt}}{\\left(t \\right)}}\\right) - 0.25 e^{\\frac{25 \\operatorname{S_{at}}{\\left(t \\right)}}{9} - 101} + 0.45\\right)}{\\left(1 + 99.0 e^{- 26.2578277150548 \\operatorname{S_{at}}{\\left(t \\right)}}\\right) \\left(0.000665 t^{2} \\left(0.34 t^{2} + 1\\right) + \\frac{1.60776201619791 \\cdot 10^{109}}{\\left(0.00421407501053519 t^{2} + 1\\right)^{2}}\\right)}$",
            "text/plain": [
              "                                      ⎛          ⎛          ⎛                2\n",
              "                                      ⎜          ⎜          ⎜         17.27⋅t \n",
              "                                      ⎜          ⎜          ⎜        ─────────\n",
              "                                      ⎜          ⎜          ⎜         2       \n",
              "                                      ⎜        4 ⎜        2 ⎜        t  + 237.\n",
              "                                      ⎜0.5985⋅t ⋅⎝- 0.01⋅t ⋅⎝0.3054⋅ℯ         \n",
              "                                      ⎜───────────────────────────────────────\n",
              "                                      ⎜                                       \n",
              "                 2⋅Sₐₜ(t)             ⎜                                       \n",
              "                 ──────── + 100       ⎝                                       \n",
              "d             2     3                                                         \n",
              "──(Sₐₜ(t)) = t ⋅ℯ               + 1 - ────────────────────────────────────────\n",
              "dt                                                                            \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "\n",
              "                         ⎞                   2                         ⎞      \n",
              "                         ⎟            17.27⋅t                          ⎟      \n",
              "─                        ⎟           ──────────                        ⎟      \n",
              "                         ⎟            2                                ⎟      \n",
              "3                        ⎟           t  + 237.3                        ⎟      \n",
              "  + 1.10462607546493e+110⎠ + 0.3054⋅ℯ           + 1.10462607546493e+110⎠      \n",
              "──────────────────────────────────────────────────────────────────────── + ───\n",
              "              2                                                               \n",
              "             t  + 273                                                      ⎛  \n",
              "                                                                           ⎝0.\n",
              "                                                                              \n",
              "──────────────────────────────────────────────────────────────────────────────\n",
              "                          ⎛          -26.2578277150548⋅Sₐₜ(t)⎞ ⎛          2 ⎛ \n",
              "                          ⎝1 + 99.0⋅ℯ                        ⎠⋅⎜0.000665⋅t ⋅⎝0\n",
              "                                                               ⎜              \n",
              "                                                               ⎜              \n",
              "                                                               ⎝              \n",
              "\n",
              "                          ⎞                                                   \n",
              "                          ⎟                                                   \n",
              "                          ⎟                                                   \n",
              "                          ⎟ ⎛                                                 \n",
              "                       2  ⎟ ⎜                                                 \n",
              "6.55966902608748e+108⋅t   ⎟ ⎜⎛               0.25        ⎞ ⎛     -0.75⋅Sₗₜ(t)⎞\n",
              "──────────────────────────⎟⋅⎜⎜0.85 + ────────────────────⎟⋅⎝1 - ℯ            ⎠\n",
              "                         2⎟ ⎜⎜              25⋅Sₐₜ(t)    ⎟                    \n",
              "                   2    ⎞ ⎟ ⎜⎜        100 - ─────────    ⎟                    \n",
              "00421407501053519⋅t  + 1⎠ ⎠ ⎜⎜                  9        ⎟                    \n",
              "                            ⎝⎝       ℯ                + 1⎠                    \n",
              "──────────────────────────────────────────────────────────────────────────────\n",
              "     2    ⎞       1.60776201619791e+109    ⎞                                  \n",
              ".34⋅t  + 1⎠ + ─────────────────────────────⎟                                  \n",
              "                                          2⎟                                  \n",
              "              ⎛                     2    ⎞ ⎟                                  \n",
              "              ⎝0.00421407501053519⋅t  + 1⎠ ⎠                                  \n",
              "\n",
              "                                \n",
              "                                \n",
              "                                \n",
              "         25⋅Sₐₜ(t)             ⎞\n",
              "         ───────── - 101       ⎟\n",
              "             9                 ⎟\n",
              " - 0.25⋅ℯ                + 0.45⎟\n",
              "                               ⎟\n",
              "                               ⎟\n",
              "                               ⎟\n",
              "                               ⎠\n",
              "────────────────────────────────\n",
              "                                \n",
              "                                \n",
              "                                \n",
              "                                \n",
              "                                "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AUnwwHlZXZw9",
        "outputId": "9a1ef192-a4ed-414f-dc9f-ed1abaca4edb"
      },
      "source": [
        "%time\n",
        "system = [CV, PA, LAI, BIO, GN, Y, SW]\n",
        "ics = {S_vt(0): 0, \n",
        "      S_at(0): 0,\n",
        "      S_lt(0): 0,\n",
        "      S_bt(0): 0,\n",
        "      S_gt(0): 0,\n",
        "      S_yt(0): 0,\n",
        "      S_wt(0): 0}\n",
        "something = dsolve(system, [S_vt(t), S_at(t),\n",
        "                S_lt(t), S_bt(t),\n",
        "                S_gt(t), S_yt(t), \n",
        "                S_wt(t)], ics=ics)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPU times: user 4 µs, sys: 0 ns, total: 4 µs\n",
            "Wall time: 7.87 µs\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xccTPn361Hdb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 341
        },
        "outputId": "b46799cf-6139-4b81-a5c8-41885bc42110"
      },
      "source": [
        "F = Matrix([CV.rhs,PA.rhs,LAI.rhs, BIO.rhs, GN.rhs, Y.rhs, SW.rhs])\n",
        "F.jacobian([S_xl, theta_vr, theta_vd, theta_vo, \n",
        "            theta_vs, theta_vq, theta_ps, theta_a,\n",
        "            theta_pr, theta_pm, theta_tr, theta_td, \n",
        "            theta_t0, theta_alpha, theta_el, theta_k,\n",
        "            theta_sr, theta_sm, theta_rue, theta_m,\n",
        "            theta_gx, theta_gb, theta_ts])"
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-100-23aba1885bb5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m             \u001b[0mtheta_t0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_alpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_el\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_k\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m             \u001b[0mtheta_sr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_sm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_rue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_m\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m             theta_gx, theta_gb, theta_ts])\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/matrices/matrices.py\u001b[0m in \u001b[0;36mjacobian\u001b[0;34m(self, X)\u001b[0m\n\u001b[1;32m    548\u001b[0m         \u001b[0;31m# m is the number of functions and n is the number of variables\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    549\u001b[0m         \u001b[0;31m# computing the Jacobian is now easy:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 550\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_new\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    551\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    552\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mlimit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/matrices/dense.py\u001b[0m in \u001b[0;36m_new\u001b[0;34m(cls, copy, *args, **kwargs)\u001b[0m\n\u001b[1;32m    304\u001b[0m             \u001b[0mrows\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflat_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    305\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 306\u001b[0;31m             \u001b[0mrows\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflat_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_handle_creation_inputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    307\u001b[0m             \u001b[0mflat_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mflat_list\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# create a shallow copy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    308\u001b[0m         \u001b[0mself\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/matrices/matrices.py\u001b[0m in \u001b[0;36m_handle_creation_inputs\u001b[0;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1067\u001b[0m                     flat_list.extend(\n\u001b[1;32m   1068\u001b[0m                         [cls._sympify(op(cls._sympify(i), cls._sympify(j)))\n\u001b[0;32m-> 1069\u001b[0;31m                          for j in range(cols)])\n\u001b[0m\u001b[1;32m   1070\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1071\u001b[0m             \u001b[0;31m# Matrix(2, 2, [1, 2, 3, 4])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/matrices/matrices.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   1067\u001b[0m                     flat_list.extend(\n\u001b[1;32m   1068\u001b[0m                         [cls._sympify(op(cls._sympify(i), cls._sympify(j)))\n\u001b[0;32m-> 1069\u001b[0;31m                          for j in range(cols)])\n\u001b[0m\u001b[1;32m   1070\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1071\u001b[0m             \u001b[0;31m# Matrix(2, 2, [1, 2, 3, 4])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/matrices/matrices.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(j, i)\u001b[0m\n\u001b[1;32m    548\u001b[0m         \u001b[0;31m# m is the number of functions and n is the number of variables\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    549\u001b[0m         \u001b[0;31m# computing the Jacobian is now easy:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 550\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_new\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    551\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    552\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mlimit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/core/expr.py\u001b[0m in \u001b[0;36mdiff\u001b[0;34m(self, *symbols, **assumptions)\u001b[0m\n\u001b[1;32m   3472\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mdiff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0massumptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3473\u001b[0m         \u001b[0massumptions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetdefault\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"evaluate\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3474\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_derivative_dispatch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0massumptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3475\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3476\u001b[0m     \u001b[0;31m###########################################################################\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/core/function.py\u001b[0m in \u001b[0;36m_derivative_dispatch\u001b[0;34m(expr, *variables, **kwargs)\u001b[0m\n\u001b[1;32m   1940\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0msympy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray_derivatives\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mArrayDerivative\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1941\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mArrayDerivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1942\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mDerivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1943\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1944\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sympy/core/function.py\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(cls, expr, *variables, **kwargs)\u001b[0m\n\u001b[1;32m   1307\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1308\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1309\u001b[0;31m                     \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"First variable cannot be a number: %i\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1310\u001b[0m                 \u001b[0mcount\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1311\u001b[0m                 \u001b[0mprev\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprevcount\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvariable_count\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: First variable cannot be a number: 150"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "VrAp9EYwHV9g",
        "outputId": "157d59c7-7d7c-4f32-ab64-536ab28f2a3b"
      },
      "source": [
        "a = Function('a')\n",
        "b = Function('b')\n",
        "da_dt = a(t).diff(t)\n",
        "db_dt = b(t).diff(t)\n",
        "f1 = Eq(da_dt, a(t)/exp(t**2))\n",
        "f1 = Eq(db_dt, a(t))\n",
        "f1\n"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} b{\\left(t \\right)} = a{\\left(t \\right)}$",
            "text/plain": [
              "d              \n",
              "──(b(t)) = a(t)\n",
              "dt             "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "qErKJIoYLV0q",
        "outputId": "1e862bcc-215d-491d-fa3c-5dac4e975d5a"
      },
      "source": [
        "fuckoff2"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d t} b{\\left(t \\right)} = a{\\left(t \\right)}$",
            "text/plain": [
              "d              \n",
              "──(b(t)) = a(t)\n",
              "dt             "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        },
        "id": "7JwKHycYIDsN",
        "outputId": "7716d1e8-2c28-4040-8907-b86e854265e0"
      },
      "source": [
        "dsolve([fuckoff1, fuckoff2], ics={a(0):0, b(0):0})"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ a{\\left(t \\right)} = 0, \\  b{\\left(t \\right)} = - C_{1} \\int\\limits^{0} e^{\\frac{\\sqrt{\\pi} \\operatorname{erf}{\\left(t \\right)}}{2}}\\, dt\\right]$",
            "text/plain": [
              "⎡                     0              ⎤\n",
              "⎢                     ⌠              ⎥\n",
              "⎢                     ⎮  √π⋅erf(t)   ⎥\n",
              "⎢                     ⎮  ─────────   ⎥\n",
              "⎢                     ⎮      2       ⎥\n",
              "⎢a(t) = 0, b(t) = -C₁⋅⎮ ℯ          dt⎥\n",
              "⎢                     ⌡              ⎥\n",
              "⎣                                    ⎦"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DYLk2HSBIVAg"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}