solving a second order nonlinear pde I would like to solve the following PDE,
$$f_{y}^{2} = 2 f f_{yy}$$
where $f= f(x,y)$ is a real function of two variables $x,y$.
My solution
: derivative of $f_{y}^{2}$ with respect to $y$ is itself, so $f_{y}^{2}= c(x)e^{y}$ and 
$$f_{y} = c(x) e^{\frac{y}{2}}$$
so, 
$f(x,y) = 2 c(x) e^{\frac{y}{2}} + d(x)$
but this does not satisfy in the equation $f_{y}^{2} = 2 f f_{yy}$ .
thanks for your help.

Hint: set $f(x,y)=g(x)h(y)$ and try and find polynomial solutions for $h(y)$.
