3
Fig 9 4
X
X’
Y’
Y
O
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MATHEMATICS
390
or
dy
x
 y dx
 = 
dy
a dx  or a = 
dy
x
dyy dx
dx (2)
Substituting the value of a from equation (2) in equation (1), we get
x2 + y2 = 2
dy
x
y dx
y
dy
dx
 
 
  
 
 
 
or
2
2
(
)
dy x
y
dx
 
 =
2
2
2
dy
xy
y dx
 
or
dy
dx  =
2
2
2
–
xy
x
y
This is the required differential equation of the given family of circles Example 8 Form the differential equation representing the family of parabolas having
vertex at origin and axis along positive direction of x-axis