# Homework Help: Another power series DE question

1. Aug 27, 2011

### JamesGoh

1. The problem statement, all variables and given/known data

Using power series, find the solution to the following DE

y" + xy' + y=0

Given data xo = 0

y(0)=1 and y'(0) = 1

2. Relevant equations

y(x) = $\sum$an(x-xo)^n for n= 0 to $\infty$

3. The attempt at a solution

Please see attached file. The part circled at the top is the answer the tutorial sheet gives.

Im thinking I could have a conceptual problem. Please feel free to point any misunderstandings I may have made

thanks

#### Attached Files:

• ###### Question 23C.pdf
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2. Aug 27, 2011

### vela

Staff Emeritus
When you reindex the first sum with n going to n+2, you need to change (n-1) to (n+1). In the y' term, you seem to have forgotten the coefficient x. It'll eliminate the need to reindex the second series. That in turn will fix your recurrence relation, hopefully.