$$0 = F''(x) + p(x) F'(x) + cF(x)\\ p(x) = ab(1-x)$$
where $a$, $b$, $c$ are non-zero constants. I'm not very strong in the theories of 2nd order ODE, so I google'ed some solution methods. Turns out that there's a lot for constant coefficients, but many standard/introductory textbooks completely skip solution methods for the part with non-constant coefficients.
I am aware of the principle of superposition, but in order to use that, I first need to find two independent solutions. How can I proceed here (or in general?)