Can You Solve This Non-linear First Order PDE with Cauchy Data?

[supermiedos]

Homework Statement

Find the general solution of Solve yu_x - xu_y = xyu²

Next, solve the Cauchy problem with the Cauchy data x = y = u

Homework Equations

The Attempt at a Solution

My teacher told us we should investigate how to solve this. The problem is we just have seen linear first order PDE, but this is non-linear! Could you please give me a hint or a name to start with?

 

[RUber]

Assume u is not zero. Apply your condition that x=y=u and divide out a factor of u.

 

[supermiedos]

Assume u is not zero. Apply your condition that x=y=u and divide out a factor of u.

I'm terrible sorry I didn't state the problem correctly. First I must find the general solution and next the condition x = y = u.