Homogenous Differential Equation

General Definition

An equation of the form

$$\frac{dy}{dx}=F(\frac{y}{x})$$

is called homogenous.

Homogenous Differential Equations

A second order differential equation $P(x)y^{\prime \prime }(x)+Q(x)y^{\prime }(x)+R(x)y(x)=G(x)$ is homogenous if $G(x)=0$.

Solutions for homogenous differential equations are found using the auxiliary equation method.