1. The problem statement, all variables and given/known data

Solve the following system of partial differential equations for u(x,y)

2. Relevant equations

3. The attempt at a solution

I am honestly not sure where to start, my lectures and tutorials this week have not been helpful at all. My guess is to take the derivative of the first equation and sub that into the second equation for y and then take the derivative of the second equation to get my final answer. But I am probably completely wrong. Any help or advice would be appreciated!