11.4.26 First order partial differential equations

Problem: Find the solution of the first-order partial differential equation under the given conditions: \[ x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}+x y \frac{\partial u}{\partial z}=0, \quad u=x^{2}+y^{2} \text { when } z=0 . \]