I have the problem:
$$x^2y''+(1/4)y=\lambda y, 1<x<e$$ $$y(1)=y(e)=0$$
And I'm trying to find a weighting function for its solutions (I already calculated the solutions and eigenvalues). If we plug $x=e^t$ we can see the equation becomes:
This seems like something I should be able to transform into Sturm-Liouville form, but since the coefficients of Y'' and $\lambda Y$ are different it doesn't seem feasible.