Definition:Auxiliary Equation

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
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation: differential equations of the second order: $(3)$ Linear equations with constant coefficients of the form $a \dfrac {\d^2 y} {\d x^2} + b \dfrac {\d y} {\d x} + c y = 0$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): auxiliary equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation: differential equations of the second order: $(3)$ Linear equations with constant coefficients of the form $a \dfrac {\d^2 y} {\d x^2} + b \dfrac {\d y} {\d x} + c y = 0$
• 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