Question

d^2f/dx^2+(ax+b)df/dx+cf=const

Could someone know an easier way to solute this ode?

Answer 1

Oliver Heaviside had a quick and easy trick for solving this kind of thing. I can't recall exactly how it went, but perhaps someone here will remember it, or try Google.

Answer 2

Laplace transformation or try to formulate some sort of tricky substitution to get it into a 1st order form. Try to play with it and see if you can get it into a constant coefficient form.