The differential equation for which `y=a cos x+b sin x` is a solution is

Options

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

Explanation

Given that, `y=acosx+bsinx`
On differentiating both sides w.r.t. x, we get
`" "(dy)/(dx)=-asinx+bcosx`
Again, differentiating w.r.t. x, we get
`" "(d^(2)y)/(dx^(2))=-asinx+bcosx`
`rArr" "(d^(2)y)/(dx^(2))=-y`
`rArr" "(d^(2)y)/(dx^(2))+y=0`