# Non-Homogenous Power series 2nd order equation

1. May 9, 2006

### diffeqnoob

I just need a hint or something to see where I start. I'm at a loss for a beginning.

Consider the non-homogenous equation
$$y'' + xy' + y = x^2 +2x +1$$

Find the power series solution about $$x=0$$ of the equation and express your answer in the form:

$$y=a_0 y_1 + a_1 y_2 + y_p$$

where $$a_0$$ and $$a_1$$ are arbitrary constants. Give only the first three nonzero terms of each of the three series$$y_1$$,$$y_2$$, and $$y_p$$

Hint: Substitute $$y = \sum_{n=0}^{\infty}a_nx^{n}$$ and equate coefficients to find $$a_n$$, $$n = 2,3,4,5$$

Last edited: May 9, 2006