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

Options

A. `(d^(2)y)/(dx^(2))-a^(2)y=0`
B. `(d^(2)y)/(dx^(2))-ay=0`
C. `(d^(2)y)/(dx^(2))+ay=0`
D. ` (d^(2)y)/(dx^(2))+a ^(2)y=0`

Answer

D

Explanation

` y= p cos ax = q sin ax`
` Rightarrow (dy)/(dx) =- p a sin ax + qa cos ax`
` Rightarrow (d^(2)y)/(dx^(2))=-p a^(2) cos ax = qa^(2) sin ax = -a^(2) y`
` Rightarrow (d^(2)y)/(dx^(2))+a^(2)y=0`