# ODE with non-constant coefficient

1. Jul 4, 2011

### PhDorBust

$$R'' + 2rR' - Rl(l+1) = 0$$, where $$R = R(r)$$ and l is a constant. This is portion of sol'n by seperation 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?

Last edited: Jul 4, 2011
2. Jul 7, 2011

### 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?

Last edited: Jul 7, 2011
3. Jul 7, 2011

### lanedance

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