This will at leat give you something to look up.
I will also give two ideas:
Idea 1: Solve the homogenous problem first.
Now find the particular solution by guessing it is a Monomial of degree 3. (do you see what it cannot have any lower degree terms.)
This will transform the equation into
This is a first order linear differential equation with contant coeffiencts.
Just FYI the usual "guess" is