(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi! I need to solve the following ODE:

[tex]xy'=1-y+x^2y^2, \qquad y(0)=1[/tex]

using a predictor-corrector method. Starting values need to be found using a Taylor method.

The exact solution is of the form [tex]\frac{\tan{x}}{x}[/tex]

2. Relevant equations

Taylor method of third order (for 1st starting value):

[tex]y_1=y_0+hy_0'+\frac{h^2}{2}y_o''+\frac{h^3}{6}y_o'''[/tex]

3. The attempt at a solution

Right here I bumped into a problem: in order to evaluate the 1st starting value (for example, if I'm using Adams-Bashforth 3rd order as a predictor and Adams-Moulton 3rd order method as a corrector) I get the following:

[tex]y'=\frac{1}{x}-\frac{y}{x}+xy^2[/tex]

Dividing with [tex]x=0[/tex] in order to get yields infinity :(. Any help would be appreciated.

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# Predictor-corrector, starting values with Taylor method

Can you offer guidance or do you also need help?

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