Let $f$ be a differentiable function of one variable and $u=\frac{x}{y}f(\frac{y}{x})$. If u satisfies a partial differential equation of the form $\frac{x}{y}u_{x} + u_{y}= G$, then who is $G$.
I tried to calculate the partial derivatives $u_{x}$ and $u_{y}$ and make a direct calculation of $G$ but I could not derive f with respect to x and y I get confused. Any hint, please.
$\textbf{hint:}$ $$ f_x = \frac{df}{du}\frac{\partial u}{\partial x}. $$ Where $u=y/x$