| The differential equation of the family of curves y = p cos (ax) + q sin (ax), where p, q are arbitrary constant, is

A.

B.

C.

D.

### Right Answer is: D

#### SOLUTION

y = p cos (ax) + q sin (ax)

y^{’}= -apsin(ax)+aqcos(ax)

y^{’’}=-a^{2}pcosax)-a^{2}qsin(ax)

y^{’’}=-a^{2}(p cos (ax) + q sin (ax))

d^{2}y/dx^{2} = -a^{2}y

d^{2}y/dx^{2}+a^{2}y = 0