Solving a Calculus Equation with u and v Variables

[implet]

Hi,

This is a question in my calculus book that is frustrating me!

By changing variables to $$u$$ and $$v$$, where $$u=\alpha(x)y$$ and $$v=y/x$$ with a suitable function $$\alpha(x)$$ to be determined, find the general solution of the equation $$x\frac{\partial f}{\partial x} - 2y\frac{\partial f}{\partial y}=6f(x,y)$$.

I can see that the LHS of the equation looks similar to the chain rule, but I can't see how to continue...

Thanks :)

 

[Hootenanny]

HINT:

Can you write $\partial f/\partial x$ and $\partial f/\partial y$ in terms of [partial] derivatives with respect to u, v, x and y?