A function $\displaystyle f$ of two variables is said to be homogeneous of degree n if $\displaystyle f(tx,ty)=t^nf(x,y)$ whenever $\displaystyle t>0$.

Show that such a function $\displaystyle f$ satisfies the equation $\displaystyle x\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y}=nf$