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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)
.
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