- #1

vanceEE

- 109

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## Homework Statement

$$xy'' + xy = 0$$

## Homework Equations

y'(0) = 0, y(0) = 1

## The Attempt at a Solution

$$ L[xy''] + L[xy] = 0$$

$$-L[-xy''] - L[-xy] = 0$$

$$-\frac{d}{dp}L[y''] - \frac{dY}{dp} = 0 $$

$$-\frac{d}{dp}(-y'(0)-py(0) + p^2Y) - \frac{dY}{dp} = 0 $$

$$\frac{d}{dp}(-p + p^2Y) + \frac{dY}{dp} = 0 $$

How would I evaluate ##p^2Y##? (does ##\frac{d}{dp}(p^2Y) = 2pY## or ## 2pY + p^2*\frac{dY}{dp}?##)

Should I end up with $$\frac{dY}{dp} = \frac{1-2pY}{p^2+1}$$?

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