# Definition:Singular Solution to Differential Equation

## Definition

A singular solution to a differential equation $E$ is a general solution to $E$ which does not contain an arbitrary constant, and hence forms a particular solution on its own.

## Also known as

Some sources refer to a singular solution as a singular integral.

## Historical Note

Singular solutions were noted by Gottfried Wilhelm von Leibniz in $1694$, and also by Brook Taylor in $1715$.

However, they are generally associated with Alexis Claude Clairaut, who reported on them in $1734$.