find recursion relation for coefficients in the series solution of xy''+(1-x)y'+2y=0
You need to show some work. Let . Write y', y'', xy', xy'' as where or and is an expression of k and 's for some . The idea is to have the th term of each series to be some coefficient times (and not, say, or ). Then write the original equation in terms of series and see what equations on you get for k = 0 and for k > 0.
Feel free to post intermediate results for checking.