How can we solve this ODE with series

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- Mar 14th 2012, 01:17 PMoasisolving ODE with series
How can we solve this ODE with series

http://img841.imageshack.us/img841/8682/80858005.png - Mar 14th 2012, 05:04 PMProve ItRe: solving ODE with series
Start by writing $\displaystyle \displaystyle \begin{align*} y = \sum_{n = 0}^{\infty}a_nx^n \end{align*} $ and substituting into the series. What could we then write $\displaystyle \displaystyle \begin{align*} y' \end{align*} $ and $\displaystyle \displaystyle \begin{align*} y'' \end{align*} $ as? Can you substitute these into the ODE and simplify?