Given the function $u=z^\alpha_1z^\beta_2+\gamma z_3+\delta$, for which non-negative values of $\alpha, \beta, \gamma, \delta$ is the function homogeneous?
I am only finding an answer where $\gamma = 0, \delta = 0$ with degree $\alpha+\beta$, but this means I lose the $z_3$ term, so it feels like I've got something wrong. Am I doing it incorrectly?