Help with PDE (first partial derivatives)

1. May 26, 2007

tpm

1. The problem statement, all variables and given/known data

I would like to know how to solve the PDE

$$\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}+\frac{\partial f}{\partial z}=g(x,y,z)$$

* f is the unknown function * g(x,y,z) is a known and smooth function

2. Relevant equations

$$divf=g$$

3. The attempt at a solution

- I have tried using 'Divergence theorem' but got no further info abut f.

- If g(x,y,z)= g(x)+g(y)+g(z) i can provide a solution othewise i have no
idea ..