# Definition:Linear Ordinary Differential Equation

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## Definition

A **linear ordinary differential equation** is an **ordinary differential equation** where all dependent variables and their derivatives appear to the first power.

Neither are products of dependent variables allowed.

## Also known as

A **linear ordinary differential equation** is frequently abbreviated to **linear ODE**.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 2.10$: Linear Equations - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**linear differential equation**