ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 15 Aug 2018 08:29:02 +0200How to solve and plot y' = x^2 + y^3https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/Hi.
My first post!
I am trying to complete this exercise:
12. 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!Mon, 13 Aug 2018 19:41:49 +0200https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/Comment by Nasser for <p>Hi.
My first post!
I am trying to complete this exercise:</p>
<ol>
<li>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!</li>
</ol>
https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/?comment=43378#post-id-43378This is Abel ODE. It should have analytical solution. https://en.wikipedia.org/wiki/Abel_equation_of_the_first_kind 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"Wed, 15 Aug 2018 03:39:38 +0200https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/?comment=43378#post-id-43378Comment by pizza for <p>Hi.
My first post!
I am trying to complete this exercise:</p>
<ol>
<li>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!</li>
</ol>
https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/?comment=43380#post-id-43380Welcome here! Could you state which way of sage you are using right now?Wed, 15 Aug 2018 08:29:02 +0200https://ask.sagemath.org/question/43369/how-to-solve-and-plot-y-x2-y3/?comment=43380#post-id-43380