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:
 * $\dfrac {\mathrm d^2 y} {\mathrm d x^2} + P \left({x}\right) \dfrac {\mathrm d y} {\mathrm d x} + Q \left({x}\right) y = R \left({x}\right)$

where:
 * $P \left({x}\right)$, $Q \left({x}\right)$ and $R \left({x}\right)$ are functions of $x$ alone (or constants)
 * $R \left({x}\right)$ is not the zero constant function.

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

Also see

 * Definition:Linear Second Order ODE
 * Definition:Homogeneous Linear Second Order ODE