How to solve and plot y' = x^2 + y^3

asked 2018-08-13 12:43:15 -0500

Hi. My first post! I am trying to complete this exercise:

  1. Although it might not be obvious from the differential equation, its solution could “behave badly” near a point x at which we wish to approximate y(x). Numerical procedures may give widely differing results near this point. Let y(x) be the solution of the initial-value problem y' = x^2 + y^3, y(1) = 1. (a) Use a numerical solver to graph the solution on the interval [1, 1.4]. (b) Using the step size h = 0.1, compare the results obtained from Euler’s method with the results from the improved Euler’s method in the approximation of y(1.4). Please help? THANK YOU!
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Comments

This is Abel ODE. It should have analytical solution. https://en.wikipedia.org/wiki/Abel_eq... and follow link to paper "Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations"

Nasser gravatar imageNasser ( 2018-08-14 20:39:38 -0500 )edit

Welcome here! Could you state which way of sage you are using right now?

pizza gravatar imagepizza ( 2018-08-15 01:29:02 -0500 )edit