Untitled4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x0*e^(-k*t)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1a\n",
    "reset()\n",
    "\n",
    "t=var('t')\n",
    "k=var('k')\n",
    "x0=var('x0')\n",
    "x=function('x')(t)\n",
    "eqd = diff(x,t)==-k*x\n",
    "sol = desolve(eqd,[x,t],[0,x0])\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1b\n",
    "plot([sol(t,0.1,10),sol(t,0.5,10),sol(t,1,10)],t,0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
  {
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   "source": []
  },
  {
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  },
  {
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  },
  {
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  }
 ],
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  "kernelspec": {
   "display_name": "SageMath 9.3",
   "language": "sage",
   "name": "sagemath"
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 "nbformat_minor": 4
}