Let $g : \mathbb R \to \mathbb R$ be a differentiable function and let $f(x,y)=x^ng(\frac {y}{x})$, where $n\in\Bbb Z^+$, show that $f$ is a solution to the PDE
$x\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y}=nf$
i know what to use, but i have a problem in the simplification, i am stopped , the far i do was:
$x\frac {\partial f}{\partial x}=nx^ng(\frac {y}{x})-x^{n-1}g´(\frac {y}{x})$
$y\frac {\partial f}{\partial y}=\frac {y}{x}g´(\frac {y}{x})$
and thats what i got, besides the sum and a vague simplification but i can´t really approach the answer