partial differential equation

Hi, I have the differential equation

$\displaystyle \frac{ \partial z }{ \partial x } + \frac{ \partial z }{ \partial y } = z^2 $. Satisfied by $\displaystyle z(x,y) $, where $\displaystyle z = f(x) $ on y=0 and x is between minus to plus infnity, show that the solution is

$\displaystyle z = \frac{f(s)}{1-f(s) t} $, where x=t+s and y=t.

I know I have to use the chain rule but I am not sure how to start. Do you have any hints you could give me to start working the solution? Thanks a lot.