Question

I have a partial differential equation, any ideas on how to solve it?

Answer 1

\[u_x=u(u_{xx}+u_{yy})\]

I need to propose a solution of the form:
\[u(x,y)=xF(\frac{ y }{ x })\] and derive the ODE for F(s), where s=y/x.

Answer 2

what class is this?

Answer 3

Differential Equations II.