ok i was working this problem and im not sure how to finish it...well i kinda have an idea..so here is the problem.

$\displaystyle y''-(x+1)y'-y=0$

and this is what i have so far....

$\displaystyle \sum_{k=0}^{\infty }(k+2)(k+1)c_{k+2}x^{k}-\sum_{k=1}^{\infty}kc_{k}x^{k}-\sum_{k=0}^{\infty}(k+1)c_{k+1}x^{k}-\sum_{k=0}^{\infty}c_{k}x^{k}$

im not sure how my book solved this for c2 and

$\displaystyle c_{k+2}=\frac{c_{k+1}+c_{k}}{k+2}$

whatever help that could be provided would be appreciated...