singular solution

A genuine solution that satisfies the equation but corresponds to no value of the general solution's constant.

A singular solution solves the differential equation directly but is not reachable from the general solution's formula for any value of its arbitrary constant.

Examples

For $y'=y^{2/3}$ , $y=0$ is a singular solution: it solves the equation, but no $C$ in $y=\left(\frac{x-C}{3}\right)^3$ produces it.