## Differential Equations and Linear Algebra (4th Edition)

$f(x,y)$ is not homogeneous of degree zero.
Given $$f(x, y)=\frac{x+7}{2 y}$$ Let \begin{aligned} f (t x, ty)&=\frac{ tx+7}{2 t y}\\ &\neq f(x,t) \end{aligned} Thus, $f(x,y)$ is not homogeneous of degree zero.