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## Homework Statement

find the series solution to y''+x^2*y'+y=0

## Homework Equations

y=summation from n=0 to infinity Cn*x^n

## The Attempt at a Solution

y=sum from 0 to inf C

_{n}x

^{n}

x^2*y'=sum from 1 to inf nC

_{ n}x

^{n+1}= sum from 2 to inf (n-1) C

_{ n-1}x

^{n}= sum from 1 to inf (n-1) C

_{ n-1}x

^{n}

y''=(n+2)(n+1)C

_{n+2}x

^{n}from 0 to infinity

basically, I cant get all three series to match at starting index n=0 and get them to have the terms x^n

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