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## Homework Statement

Find the first five non-zero terms of the power series solution to

d

^{2}y/dx

^{2}-xy=0 about x=-2; y(-2)=1;y'(-2)=1/2

## Homework Equations

... calculus in general?

and the taylor expansion of y(x) is - assuming remainder term is zero:

[itex]\sum[/itex]y

^{(n)}(-2)/n! *(x+2)

^{n}(n from 0 to infinity)

and y''(x) is:

[itex]\sum[/itex]y

^{(n)}(-2)/(n-2)! *(x+2)

^{n-2}(n from 2 to infinity

## The Attempt at a Solution

I let x'=x+2, giving:

[itex]\sum[/itex]y

^{(n)}(-2)/(n-2)! *(x')

^{n-2}-x'[itex]\sum[/itex]y

^{(n)}(-2)/n! *(x+2)

^{n}+2[itex]\sum[/itex]y

^{(n)}(-2)/n! *(x+2)

^{n}

(parameters of first sum are from 2 to infinity, of second two sums from 0 to infinity)

But I'm not sure what to do from here - do I need to find y?