(7)
�Note  The order of a differential equation representing a family of curves is
same as the number of arbitrary constants present in the equation corresponding to
the family of curves Example 4 Form the differential equation representing the family of curves y = mx,
where, m is arbitrary constant Solution We have
y = mx (1)
Differentiating both sides of equation (1) with respect to x, we get
dy
dx  = m
Substituting the value of m in equation (1) we get 
dy
y
x
dx  
or
dy
x dx  – y = 0
which is free from the parameter m and hence this is the required differential equation