- #1

Saladsamurai

- 3,020

- 7

## Homework Statement

Solve xy' - y = x

^{3}(1) by using variation of parameters.

## 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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