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 Example 5 Form the differential equation representing the family of curves
y = a sin (x + b), where a, b are arbitrary constants