Homogeneity of $f(x,y) = \frac{3x^2y}{x^2+y^2}$

Question

Regarding my previous question about the function $f(x,y)$ somebody claimed that $f(ax,ay)=af(x,y)$ is only true for "homogeneous" $x$ and $y$. Does anyone know what "homogeneous" means in this context?

Answer 1

A function $f(x,y)$ of two variables is called homogeneous if $f(ax,ay)=a^nf(x,y)$