Chapter 8.4, Problem 21P

As in text just before (4.11), show that

(a) $x^2-5xy+y^3/x$ is a homogeneous function of degree 2;

(b) $x^{-1}\left(y^4-x^{3}y\right)-x{y}^2\sin (x/y)$ is homogeneous of degree 3;

(c) $x^2{y}^3+x^5\ln (y/x)-y^6/\sqrt{x^2+y^2}$ is homogeneous of degree 5;

(d) $x^2+y,x+\cos y,$ and $y+1$ are not homogeneous.

See Chapter 4, Section 13, Problem 1 for a more general definition of a homogeneous function of any number of variables.