Hi, 1. The problem statement, all variables and given/known data I have the following ODE: y′′−2xy′+2αy=0 I'd like to determine the first three eigenfunctions. 2. Relevant equations 3. The attempt at a solution The solution y(x) may be recursively represented as: an+2=an(2n−2α)/[(n+2)(n+1)] I have found the eigenvalues to be −2α, however I find the manner whereby the eigenfunctions are determined to be rather perplexing. I'd sincerely appreciate an explanation. For instance, I know that for α=0, a2=a0(0−0)/2, but why would that entail y0(x)=a0? I mean, how was that derived?