Question

1st order partial differential equation?
Consider the following Cauchy initial value problem:

x(∂u/∂x) - y(∂u/∂y) = u, u(x,y) = x^2 on y = x, 1<=y<=2

If u=u(x,y) is a solution to the above PDE, determine the following parametric equations:
x = x(s,t)
y = y(s,t)
u = u(s,t)

By eliminating s and t between the above parametric equations show that the solution to the initial value problem is given by:
u(x,y) = x*sqrt(xy)

Thanks in advance!