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

Find the Taylor expansion y(x) satisfying: y'(x) = 1 - xy

2. Relevant equations

3. The attempt at a solution

So I need expressions for y''(x), y'''(x), ...etc

I can find y''(x)=-y-xy' by differentiating implicitly.

By setting y'(x)=z, then dz/dx = δz/δx+(δz/δy)(dy/dx)

However when I use the same method to try and find y'''(x) I have problems:

- partial differential of y'(x) ?

- is the (dy/dx) from the implicit formula still dy/dx or the second differential?

[Ans: -2y'-xy'']

Please tell me the technique, or give me a reference, that is used to find y'''(x) in this example?

Thanks!

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# Homework Help: Taylors series for simple ODE

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