Find $f(x)$ using Mean Value Theorem.

Question

Given $f:\mathbb{R} \mapsto \mathbb{R}$ such that $f(0)=3$ and

$$f'(x) + 2f(x) = 4 -8x \quad x\in \mathbb{R}$$

What is $f(x)$?

Many thanks!

Answer 1

in a first step solve the equation $$f'(x)+2f(x)=0$$ with $$f(x)=e^{\lambda x}$$