{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Script to illustrate how to draw direction field with supplied command\n",
    "#draw_dirfield().\n",
    "\n",
    "#Define right side of ODE u' = f(t,u)\n",
    "def f(t,u):\n",
    "    return t*cos(u) - sin(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load in supplied command for direction fields\n",
    "load('draw_dirfield.sage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Construct phase portrait on range 0 <= t <= 5, 0 <= u <= 5.\n",
    "draw_dirfield(f, [0,5,0,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Construct phase portrait with solutions satisfying u(1) = 2, u(2) = 3,\n",
    "#and u(3) = 1\n",
    "draw_dirfield(f, [0,5,0,5], [[1,2],[2,3],[3,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}