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Math Help - Series Solution

  1. #1
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    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
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  2. #2
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    Re: Series Solution

    Quote Originally Posted by weber View Post
    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...
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