# Definition:Nonhomogeneous Linear Second Order ODE

## Definition

A nonhomogeneous linear second order ODE is a differential equation which is in (or can be manipulated into) the form:

$\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = \map R x$

where:

$\map P x$, $\map Q x$ and $\map R x$ are functions of $x$ alone (or constants)
$\map R x$ is not the zero constant function.

That is, a nonhomogeneous linear second order ODE is a linear second order ODE which is not homogeneous.