Example 5 Form the differential equation representing the family of curves
y = a sin (x + b), where a, b are arbitrary constants Solution We have
y = a sin(x + b) (1)
Differentiating both sides of equation (1) with respect to x, successively we get
dy
dx  = a cos (x + b) (2)
2
d y2
dx
 = – a sin(x + b)