1. The problem statement, all variables and given/known data (x-1)y'' - xy' + y = 0, y=e^x is a solution 2. Relevant equations 3. The attempt at a solution Assume the second solution is of the form ve^x, where v' = (y^'2)e^-int[-x/(x-1)] So v' = e^(-2x)e^(x+ln|x-1|) = e^(ln|x+1|-x) Then, this second solution must be (e^x)(e^(ln|x-1|-x)) =e^(ln|x-1) =x-1 But, this is no solution to the DE. What went wrong? Thank you. NEVERMIND, I forgot to integrate v'. What was I thinking?