Finding f(x) for f'(x)f(x) = f'(x) + f(x) + 2x^3 + 2x^2 - 1

[viciousp]

Homework Statement

find f(x) satisfying the equation:

f'(x)f(x)=f'(x)+f(x)+2x^3+2x^2-1

Homework Equations

The Attempt at a Solution

I have the general idea of what to do but need to know if f(x) is a degree 2 polynomial for this problem to work. I assume it is so you can get to a third power through multiplying f(x) by f'(x), and after that you just make many substitutions. Am I on the right track?

 

[viciousp]

I worked it out and it seems to be a=1, b=1, c=1 so f(x)=x^2+x+1 and f'(x)=2x+1. it seems to work out when plugged in, can anyone confirm this

 

[dirk_mec1]

confirmed!