# Definition:Auxiliary Equation

(Redirected from Definition:Characteristic Equation of ODE)

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## Definition

Let:

- $(1): \quad y'' + p y' + q y = 0$

be a constant coefficient homogeneous linear second order ODE.

The **auxiliary equation** of $(1)$ is the quadratic equation:

- $m^2 + p m + q = 0$

## Also known as

Some sources refer to the **auxiliary equation** as the **characteristic equation** of $(1)$.

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## Also see

- Results about
**auxiliary equations**can be found**here**.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.17$: The Homogeneous Equation with Constant Coefficients - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**auxiliary equation** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**auxiliary equation** - 2009: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(9th ed.) ... (next): $\S 3.1$ - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**auxiliary equation**