Clairaut's Differential Equation

Clairaut's differential equation has the form

y=y'x+g(y')

. Its general solution is a one-parameter family of straight lines

y=Cx+g(C)

. The singular solution is obtained by eliminating the parameter

C

from the equations

y=Cx+g(C)

and

x=-g'(C)

.

Izidor Hafner