Difficult calculus problem

[Panphobia]

Dont tell me that this question isn't hard because, I have not learned differential equations yet so I do not know what to do.

code:

If: f''(x) + f'(x) - 2f(x) = 4x - 4 F''(x) != 0 Find f(x)

[Dreadnought]

Ignore the condition of f'' not 0, can you solve that?

Then consider g(x) = exp(x), what is g''(x) + g'(x) - 2g(x).

EDIT: It's not necessarily that the question is really hard, but rather tricky, once you see the trick it's not so bad.