# Differential Equations: Non-homogeneous Series Expansion

1. Dec 11, 2011

### Bryon

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

y'' + y' + y = 1 + x + x2

2. Relevant equations

y = Ʃ CN*xN N starts at 0
y' = Ʃ N*CN*x(N-1) N starts at 1
y'' = Ʃ N*(N-1)*CN*x(N-2) N starts at 2

3. The attempt at a solution[/]
I know how solve the equations using series when the equation would equal to 0. My main question about using series on a non-homogeneous differential equation is whether or not the varialbes on the right side have the Cx coefficients? Or would they be paired up with the x, x2, etc? I think I need some quick clarification on this.

Thanks!

2. Dec 11, 2011

### LCKurtz

The Cn's only appear in your expressions for y and its derivatives. But you must take the powers of x on the other side into account for your recursion formulas. I assume you know that series isn't the easiest way for this problem.

3. Dec 11, 2011

### Bryon

Thanks for clearing that up. The instructor covered only homogenous problems, and when I ran into one of these I was not entirely sure how to solve it with series.