(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) (3)
Eliminating a and b from equations (1), (2) and (3), we get
2
d y2
y
dx
+
 = 0 (4)
which is free from the arbitrary constants a and b and hence this the required differential
equation