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

Solve xy' - y = x^{3}(1) by using variation of parameters.

3. The attempt at a solution

Solving the homogeneous version of (1) gives

y_{h}= c_{1}x

Now we are to seek

y_{p}= A(x)*x (2)

from (2)

y'_{2}= A'*x +A

plugging into (1) we have:

x[A'*x + A] - Ax = x^{3}

A'x^{2}= x^{3}

A' = x

=> A(x) = x^{2}/2 +C_{2}

=>y_{p}= C_{2}x + x^{3}/2

Oh ... nevermind!

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# Homework Help: Variation of Parameters on a 1st Order DE

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