The task is to transform the following equation $x \frac{dx}{dz}+y \frac{dz}{dy} =0$ into new one with independent variables taking $\varphi=\varphi(a,b)$ as a new function, for $a=\frac{y}{x}, b=y, \varphi=yz-x$.
This task was given us as an example of what to expect on exam, however I've no idea of how to deal with this kind of tasks. Would be grateful for any help, especially first steps or ways of getting correct answer, as I've solved several tasks which involved variable change, however have never seen any with a new function, beside variables..