# Definition:Differential Equation/Solution/Particular Solution

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## Definition

Let $\Phi$ be a differential equation.

Let $S$ denote the solution set of $\Phi$.

A **particular solution** of $\Phi$ is the element of $S$, or subset of $S$, which satisfies a particular boundary condition of $\Phi$.

## Also known as

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

A **particular solution** is also known as a **specific solution**.

Some sources refer to a **particular solution** as a **particular integral**.

## Also see

- Definition:Solution of Differential Equation
- Definition:General Solution of Differential Equation
- Definition:Singular Solution to Differential Equation

## Sources

- 1956: E.L. Ince:
*Integration of Ordinary Differential Equations*(7th ed.) ... (previous) ... (next): Chapter $\text {I}$: Equations of the First Order and Degree: $2$. Integration - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 2$: General Remarks on Solutions - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**differential equation** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**differential equation** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**particular solution**