# 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.