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Math Help - How to solve this second order equation using power series method?

  1. #1
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    How to solve this second order equation using power series method?

    Find the power series solutions of the equation:

    (2x2)y'' + (3x)y' - (x2 + 1)y = 0



    Any help would gladly be appreciated.
    Last edited by redhotman225; November 26th 2012 at 07:39 PM.
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  2. #2
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    Re: How to solve this second order equation using power series method?

    Start by writing \displaystyle \begin{align*} y = \sum_{ k = 0 }^{\infty} c_k \, x^k \end{align*}, which means \displaystyle \begin{align*} y' = k\, c_k \, x^{k-1} \end{align*} and \displaystyle \begin{align*} y'' = k\left( k - 1 \right) c_k \, x^{k - 2} \end{align*}.

    Substitute these in and perform some algebraic manipulation. What can you come up with?
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