Question:
By changing the variables from $x$, $y$ to $s$, $t$, where $s = xy$ and $t = x/y$, solve the equation
$x\frac{\partial u}{\partial x}-y\frac{\partial u}{\partial y} = 2x^2$
The only part of solving this type of equation I am having trouble seeing how to do is how to get the values of $u_x$ and $u_y$ but I can carry on from there to solve the equation.