Another power series DE question

[JamesGoh]

Homework Statement

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

Homework Equations

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

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

 

[vela]

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.