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!
$\displaystyle y'' - 4xy' -4y = e^x$
Start by writing $\displaystyle \displaystyle \begin{align*} y = \sum_{n = 0}^{\infty}c_n x^n \end{align*}$, then use this to get sums for $\displaystyle \displaystyle \begin{align*} y' \end{align*}$ and $\displaystyle \displaystyle \begin{align*} y'' \end{align*}$. Also write $\displaystyle \displaystyle \begin{align*} e^x = \sum_{n = 0}^{\infty}\frac{x^n}{n!} \end{align*}$.
See if you can simplify...