(2)
Substituting the value of 4a from equation (2)
in equation (1), we get
y2 =
2
( )
ydy
x
dx
⎛
⎞
⎜
⎟
⎝
⎠
or
2
2
dy
y
−xy dx
 = 0
which is the differential equation of the given family
of parabolas Fig 9 5
© NCERT
not to be republished
DIFFERENTIAL EQUATIONS
391
EXERCISE 9 3
In each of the Exercises 1 to 5, form a differential equation representing the given
family of curves by eliminating arbitrary constants a and b