Clairaut's Differential Equation

equation

y(x)x

′

y

(x)-

2

′

y

(x)

parameter of general solution

1

show general solution plot

show singular solution plot

general solution:

cx-

2

c

singular solution(s):



2

x

4



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)

.