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$$ y''+y'+xy=0 $$ I can't seem to get $y_1$ or $y_2$ to have any sort of pattern. I understand the technique to it but have no idea what the general solution is.

The equation I have for the coefficients is $C_{k+2}=(-(k+1)\cdot C_{k+1}-C_{k-1})/((k+2)\cdot(k+1))$ I'm pretty sure that is right, but not certain.

Also, $C_{2}=-C_{1}/2$

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    Hi, Welcome to MSE =) I am not sure I corrected your equation for your coefficients correctly, perhaps you should make sure I didn't make any typo. It wasn't quite clear what was written there before!2011-11-30
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    Suggestion: pick some simple values for $C_0$ and $C_1$, calculate the next few $C_i$ and, if you don't see a pattern, post the numbers here and maybe someone else will see it. Alternatively, multiply all the values you got by the LCM of their denominators, so you have an integer sequence, which you can look up in the Online Encyclopedia of Integer Sequences.2011-12-01

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