# Definition:Differential Equation/Solution

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## Contents

## Definition

Let $\Phi$ be a differential equation.

Any function $\phi$ which satisfies $\Phi$ is known as **a solution** of $\Phi$.

Note that, in general, there may be more than one **solution** to a given differential equation.

On the other hand, there may be none at all.

## Also known as

A **solution of a differential equation** can also be referred to as a **solution to a differential equation**.

Such a **solution** is known as a **particular solution**.

Some sources refer to such a **solution** as a **specific solution**.

## Also see

- Definition:Solution Set of Differential Equation: the set of all
**solutions**to a differential equation.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.2$: General Remarks on Solutions - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**differential equation** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**differential equation**