It is a particular case of the Lagrange differential equation.
It is named after the French mathematician Alexis Clairaut, who introduced it in 1734.
[1] To solve Clairaut's equation, one differentiates with respect to
Substituting this into the Clairaut's equation, one obtains the family of straight line functions given by the so-called general solution of Clairaut's equation.
, the so-called singular solution, whose graph is the envelope of the graphs of the general solutions.
The singular solution is usually represented using parametric notation, as
The parametric description of the singular solution has the form where