MathDB
Miklós Schweitzer 1961- Problem 7

Source:

December 1, 2015
college contests

Problem Statement

7. For the differential equation
2ux2+2uy2=22uxy \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}= 2\frac{\partial^2 u}{\partial x \partial y}
find all solutions of the form u(x,y)=f(x)g(y)u(x,y)=f(x)g(y). (R. 14)