A little PDE solving Guys I really don't know what to do, I apply the method of characteristics, but the system of equations it gave me looks unfamiliar and complicated. Any hint on how to approach this?
Find a solution of the first order quasi-linear partial differential equation:
$$z(x +z)\frac{\partial z}{\partial x} + y(y +z)\frac{\partial z}{\partial y} =0$$ such that it passes through points of parabolic cylinder $z = \sqrt y$ and $x=1$.
Thanks.

The result below is an implicit equation :
$$z^3+x\,z^2+(x-2)\,y\,z-y=0$$
The solution could be expressed on explicit form in solving the cubic equation for $z$.

