# Definition:Homogeneous Linear Second Order ODE with Constant Coefficients

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## 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:

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

## Also see

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 18$: Basic Differential Equations and Solutions: $18.7$: Linear, homogeneous second order equation - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.17$: The Homogeneous Equation with Constant Coefficients