Question

What is a homogeneous differential equation?

Answer 1

Homogeneous differential equation.

Differential equation$\frac{dy}{dx}=f(x,y)$ is a homogeneous differential equation, if the function $f(x,y)$ is a homogeneous function.

The homogeneous function of degree $n$ is expressed as:

$f(kx,ky)=k^{n}f(x,y)$

For example:

$\frac{dy}{dx}=\frac{x^2+y^2}{xy},\frac{dy}{dx}=\frac{3x+y}{x-y}$