Definition:Differential Equation/Solution/Particular Solution

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 to 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): differential equation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): particular solution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): particular solution
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): particular solution