ODE with non-constant coefficient

[PhDorBust]

$$R'' + 2rR' - Rl(l+1) = 0$$, where $$R = R(r)$$ and l is a constant. This is portion of sol'n by separation by variables to laplace's equation in spherical coordinates.

I tried laplace transform, but reached integral that I don't think admits analytic sol'n.

$$F'(s) + F(s)[\frac{1 + l(l+1)}{s} - s] = sA + B$$, where R(0) = A, R'(0) = B.

What am i missing? Is series sol'n the only way?

 

[lanedance]

series sounds like a good idea for this type of problem asnd would be my first approach - is there reason you don't want to use it, or is an analytic expression just going to be simpler to deal with?

 

[lanedance]

froma mathematica check it looks like the solutions involve hermite polynomials and other complex functions