I'm studying differential equations and in one question on a sheet the teacher gave us for practice I'm asked to find a 3rd degree linear differential equation. I know 2 particular solutions and the solution of the associated homogeneous solution.
My question is: how do I use the particular solutions, I can write a polynome using the homogeneous and another one using the particular ones. I dont know what to do from here. I have a resolution of this question, but none of my colleagues is able to explain it, they just memorized the process for the evaluation, I'm trying to understand it. Theres a photo of the resolution.