Suppose f is a function such that it is infinitely differentiable and homegeneous of degree $\displaystyle n \in \mathbb{N}$,show that

$\displaystyle x^{2}\frac{\partial^{2}f}{\partial x^{2}}+2xy\frac{\partial^{2}f}{\partial x\partial y}+y^{2}\frac{\partial^{2}f}{\partial y^{2}}=n(n-1)f(x,y)$

Hi all,

for the above question, what is the link of f' in terms of f and n?? I tried using the rate of change quotient here, but I cant get the prove done. I think that if i can find f' in terms of f and n, then f'' should be far. Thanks.