I've no clue how to get started .I'am unable to even understand what the hint is saying.I need your help please.
Given $u = f(ax^2 + 2hxy + by^2), \qquad v = \phi (ax^2 + 2hxy + by^2),$ then prove that
$\frac{\partial }{\partial y} \left ( u\frac{\partial u }{\partial x} \right ) = \frac{\partial }{\partial x}\left ( u \frac{\partial v}{\partial y} \right ).$
Hint. Given $u = f(z),v = \phi(z), \text{where} z = ax^2 + 2hxy + by^2$