# Solving DE using power series

1. Oct 22, 2009

### Fuzedmind

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

Solve this equation using power series: y'' + y = x

2. Relevant equations

none

3. The attempt at a solution

I am confused about the x on the RHS of the equation. If the equation was y'' + y = 0, I would have no problem solving it. I am just a little confused about how the x fits into the equation for cn.

if the equation were y'' + y = 0, then cn + 2 = cn/(n+1)(n+2). How does the x fit into this?

2. Oct 22, 2009

### Staff: Mentor

You should be able to split up the series you get into three parts. One of those parts will be very short, with just a single term.

Show us what you have for your series.

3. Oct 22, 2009

### Fuzedmind

I'm a newb and don't know how to use this website, so here goes:

SUM[ (n+2)(n+1)cn+2xn] + SUM[cnxn] = x

4. Oct 22, 2009

### Fuzedmind

$$\ \ \sum_{n=0}^{\infty}{(n+2)(n+1)c_{n+2}x^n} \ \ + \ \ \sum_{n=0}^{\infty}{c_{n}x^n} \ \ = x$$

Here it is in the non-retarded version

Last edited: Oct 22, 2009
5. Oct 22, 2009

### Staff: Mentor

Try expanding your two series and then grouping the results by powers of x. Be sure to take the x on the right side into account.

6. Oct 24, 2009

### Fuzedmind

I kind of understand what you're saying, but could you try being a little more specific? I am terrible with series.