# Series Solutions to a 2nd Order Diff. Eq.

1. Jul 15, 2015

### RyanTAsher

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

y'' + y' + xy = 0

Just want to make sure I understand this completely, I had a bit of trouble towards the end, and thought the -29/600 was a little weird of a fraction to be right. I wasn't given a correct answer to base mine off, so I'm not sure if I'm doing this all right.

2. Relevant equations

3. The attempt at a solution

2. Jul 15, 2015

### fzero

First off, you should always be able to verify that the solution you've derived is actually a solution by plugging it back into the DE and comparing terms order by order. Second, and more directly relevant, in your 5th line, you have lost the factor of $x$ in the 3rd, $xy$ term. Correcting this will significantly change the recursion relations.

3. Jul 15, 2015

### FactChecker

I think you forgot to increase the exponent of x in the last summation of line 5 when you multiplied through by x.