Series Solutions to a 2nd Order Diff. Eq.

[Destroxia]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[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.

 

[FactChecker]

I think you forgot to increase the exponent of x in the last summation of line 5 when you multiplied through by x.
Already answered above. How come I can't delete this?

 

[Destroxia]

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.

I think you forgot to increase the exponent of x in the last summation of line 5 when you multiplied through by x.
Already answered above. How come I can't delete this?

Thank you both, I will rework it and post my answer here.