A singular solution of a differential equation is a solution that cannot be obtained by assigning values to the constants of integration in the equation's general solution. For a first-order equation, a singular solution is often an envelope of the one-parameter family represented by the general solution. It must be checked directly in the original differential equation because eliminating the parameter can introduce extraneous candidates.
Singular Solution
See also
Clairaut's Differential Equation, General Solution, Particular SolutionExplore with Wolfram|Alpha
References
Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 9th ed. Hoboken, NJ: Wiley, 2009.Cite this as:
Weisstein, Eric W. "Singular Solution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SingularSolution.html