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!

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

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- Jun 24th 2012, 02:04 PMweberSeries 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!

$\displaystyle y'' - 4xy' -4y = e^x$ - Jun 24th 2012, 07:23 PMProve ItRe: Series Solution
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...