# recursion relation, please help

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• May 13th 2012, 10:11 AM
jsmit037
recursion relation, please help
find recursion relation for coefficients in the series solution of xy''+(1-x)y'+2y=0
• May 13th 2012, 11:55 AM
emakarov
Re: recursion relation, please help
You need to show some work. Let $y=\sum_{k=0}^\infty a_kx^k$. Write y', y'', xy', xy'' as $\sum_{k=k_0}^\infty b_kx^k$ where $k_0=0$ or $k_0=1$ and $b_k$ is an expression of k and $a_i$'s for some $i$. The idea is to have the $k$th term of each series to be some coefficient times $x^{k}$ (and not, say, $x^{k+1}$ or $x^{k-1}$). Then write the original equation in terms of series and see what equations on $a_k$ you get for k = 0 and for k > 0.

Feel free to post intermediate results for checking.