What is the solution for the function in the given equation?

[tombk2]

Homework Statement

$$f:\Re\rightarrow\Re$$
$$e^xf(x)+e^xf\prime(x)=f(x)$$
Find f(x)

Homework Equations

The Attempt at a Solution

i don't know if $$f(x)\neq 0$$ so i can't divide by $$f(x)$$ which would make things pretty simple.

 

[cse63146]

Try this:

put all f '(x) on the left side, and f(x) on the right side