# Definition:Homogeneous Linear Second Order ODE with Constant Coefficients

## Definition

A homogeneous linear second order ODE with constant coefficients is a second order ODE which can be manipulated into the form:

$y'' + p y' + q y = 0$

where $p$ and $q$ are real constants.

Thus it is a homogeneous linear second order ODE:

$y'' + \map P x y' + \map Q x y = 0$

where $\map P x$ and $\map Q x$ are constant functions.

## Also known as

The word ordering may change, for example:

constant coefficient homogeneous linear second order ODE

Abbreviations can be used:

constant coefficient homogeneous LSOODE

and so on.

## Also presented as

Such an equation can also be presented in the form:

$\dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = 0$