Chapter 2.6, Problem 43E

To determine

a)

To show:

The equation $\frac{dy}{dx}=f\left(x,y\right)$ is homogenous if $f\left(tx,ty\right)=f\left(x,y\right)$.

To determine

(b)

To show:

The function $M\left(x,y\right)dx+N\left(x,y\right)dy=0$ is homogenous if $M\left(x,y\right)$ and $N\left(x,y\right)$ both are homogenous of same order.