# Definition:Linear Second Order Ordinary Differential Equation

## 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

• Results about linear second order ODEs can be found here.