(2)
Differentiating both sides of equation (2) with respect to x, we get
2
2
2
xdy
y
y
d y
dy
dx
x
dx
dx
x
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
  
 
 
 
 = 0
or
2
2
2
–
d y
dy
dy
xy
x
y
dx
dx
dx
 
 
 
 
 
 
 
 = 0 (3)
which is the required differential equation Example 7 Form the differential equation of the family
of circles touching the x-axis at origin Solution Let C denote the family of circles touching
x-axis at origin