find recursion relation for coefficients in the series solution of xy''+(1-x)y'+2y=0

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- May 13th 2012, 09:11 AMjsmit037recursion relation, please help
find recursion relation for coefficients in the series solution of xy''+(1-x)y'+2y=0

- May 13th 2012, 10:55 AMemakarovRe: recursion relation, please help
You need to show some work. Let $\displaystyle y=\sum_{k=0}^\infty a_kx^k$. Write y', y'', xy', xy'' as $\displaystyle \sum_{k=k_0}^\infty b_kx^k$ where $\displaystyle k_0=0$ or $\displaystyle k_0=1$ and $\displaystyle b_k$ is an expression of k and $\displaystyle a_i$'s for some $\displaystyle i$. The idea is to have the $\displaystyle k$th term of each series to be some coefficient times $\displaystyle x^{k}$ (and not, say, $\displaystyle x^{k+1}$ or $\displaystyle x^{k-1}$). Then write the original equation in terms of series and see what equations on $\displaystyle a_k$ you get for k = 0 and for k > 0.

Feel free to post intermediate results for checking.