Definition:Singular Solution to Differential Equation

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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

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 $1734$.