# Definition:Linear Second Order Ordinary Differential Equation

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## Definition

A **linear second order ordinary differential equation** 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, as is indicated by the notation, $\map P x$, $\map Q x$ and $\map R x$ are functions of $x$ alone (or constants).

## Also presented as

A **linear second order ordinary differential equation** can also be presented as:

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

## Also known as

The order of adjectives can be varied, for example: **second order linear ordinary differential equation**.

## Also see

- Definition:Linear Second Order ODE with Constant Coefficients
- Definition:Homogeneous Linear Second Order ODE

- Results about
**linear second order ODEs**can be found**here**.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 2.10$: Linear Equations - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.14$: Second Order Linear Equations: Introduction