Partial Differential Equation

Consider the equation

$\displaystyle 4y^2u_{xx} + 2(1-y^2)u_{xy} - u_{yy}- \frac{2y}{1 + y^2}(2u_x - u_y) = 0 $

Derive the transformation $\displaystyle \xi = x + 2y, \eta = x -\frac{2}{3} y^3 $ ,show that the equation reduces to $\displaystyle \omega_{\xi \eta} = 0 $ where $\displaystyle \omega(\xi, \eta) = u(x(\xi, \eta), y(\xi,eta)) $ , and find the general solution.

I am a part-time maths student, so I havent done any calculus courses for about a year and a half (although I did a numerical analysis course last semester that looked at numerical methods for ODE's and PDE's) and I'm really rusty :(

This is my last semester, so I would really appreciate it if someone could help me understand this.

Thanks