# Definition:Singular Solution to Differential Equation

(Redirected from Definition:Singular Integral)

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## 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**.

## Also see

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

## 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 $1734$.

## 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