$\displaystyle \psi'(y)+y^2\psi'(y)-\lambda\psi(y)=0$
How can I approach this?
The Cauchy Euler method didn't work.
Really? I thought you could have a CE equation of any order. You just needed to have the appropriate power of x multiplying the corresponding order of differentiation. The wiki certainly seems to indicate that. There's nothing preventing a CE equation from being third order, or fourth. Why not first-order?...Cauchy Euler Equations are second order equations...