I'm looking for the particular solution of an nonhomogeneous second order differential equation. The inhomogeneous term is a function of the form: 1u1u. I've tried to find the particular solution by the "varying constant technique". That is, if the solution of the homogeneous equation is C 1F1(a,b,u)C 1F1(a,b,u), I look for a particular solution of the form C~(x) 1F1(a,b,u)C~(x) 1F1(a,b,u). The problem is that this method is not giving me a good result.
Is there any way of trying to get the particular solution by hand (taking into account that the inhomogeneous term is of the form 1/u)?
Thanks!