Proving homogeneity of dy/dx=(x+3y)/(x-y)

[karush]

$\dfrac{dy}{dx}=\dfrac{x+3y}{x-y}$
ok well following the book example: divide numerator and denominator by x

$\dfrac{dy}{dx}=\dfrac{1+3\dfrac{y}{x}}{1-\dfrac{y}{x}}$

apparently, thus this is homogeneous but not sure why?

next solve the DE:unsure:

 

[skeeter]

Homogeneous Differential Equations (mathsisfun.com)

 

[karush]

Segerstrom Science Center
Azusa Pacific University
alma mater 1970

never did any pencil sketch before
so this is my first one