# Definition:Nonhomogeneous Linear Second Order ODE

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## 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.

## Also see

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.14$: Second Order Linear Equations: Introduction