See here.

I think Laplace Transforms can be used to take care of these nasties IFF there are initial conditions given. See here.Also, is there a general method for solving second order homogeneous DE with non-constant coefficients that are NOT in the Cauchy-Euler form and that does not use power series? Thanks !

Otherwise I'm not quite sure of any other technique besides using power series...

I would consider conducting a Google search