# Series Solution

• Jun 24th 2012, 03:04 PM
weber
Series Solution
Hey!

I'm having problems with finding the general solution of this DE,

using series.

I have readed the Zill book, but I don't know how to start solving.

Any help is appreciated!

$y'' - 4xy' -4y = e^x$
• Jun 24th 2012, 08:23 PM
Prove It
Re: Series Solution
Quote:

Originally Posted by weber
Hey!

I'm having problems with finding the general solution of this DE,

using series.

I have readed the Zill book, but I don't know how to start solving.

Any help is appreciated!

$y'' - 4xy' -4y = e^x$

Start by writing \displaystyle \begin{align*} y = \sum_{n = 0}^{\infty}c_n x^n \end{align*}, then use this to get sums for \displaystyle \begin{align*} y' \end{align*} and \displaystyle \begin{align*} y'' \end{align*}. Also write \displaystyle \begin{align*} e^x = \sum_{n = 0}^{\infty}\frac{x^n}{n!} \end{align*}.

See if you can simplify...