Solve the following differential equation:

so starting off with the auxiliary equation I have:

where the only available solution is

so I would have:

working on the particular solution I let

substituting for I come up

(this is the part that I get stuck on) Since is a polynomial of third degree I would have:

where

substituting I get:

, then

so and where I don't think that I'm approaching it correctly since i have 4 unknowns.

any help would be greatly appreciated.