Howdy folks, got stumped by this one, let me know if you have any ideas. It's in the Green's Functions/Variation of Parameters section of Birkhoff and Rota.
Show that if a second order inhomogeneous DE is satisfied by x^2 and (sin(x))^2, then it has a singular point at the origin.
You can't show this by plugging in the solutions directly and solving for p0(x) in L[u] = p0(x)u'' + p1(x)u' + p2(x)u = r(x) as you get an indeterminant form. I am genuinely stumped.