# Definition:Homogeneous Linear Second Order ODE

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## Definition

A **homogeneous linear second order ODE** is a differential equation which is in (or can be manipulated into) the form:

- $\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = 0$

where, as is indicated by the notation, $\map P x$ and $\map Q x$ are functions of $x$ alone (or constants).

## Also see

- Results about
**homogeneous linear second order ODEs**can be found**here**.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.14$: Second Order Linear Equations: Introduction