1. The problem statement, all variables and given/known data A function F of n real variables is called homogeneous of degree r if it satisfies F(tx_1, tx_2, ..., tx_n) = (t^r)F(x_1,x_2,...,x_n) By differentiation with respect to t, show that a function F is an eigenfunction of the operator: x^1 ∂/∂x_1 + ... + x^n ∂/∂x_n and find the eigenvalue 2. Relevant equations 3. The attempt at a solution Here's what I've done so far: Differentiating with respect to t: dF(tx)/dt = rt^(r-1)F(x) But what do they mean by asking me to show it is an eigenfunction of the operator, and how would I go about calculating the eigenvalue? Any hints in the right direction would be super! Thanks!