Verify that the function`y = a cos x + b sin x`, where, a, `b in R`is a solution of the differential equation `(d^2y)/(dx^2)+y=0`.

Explanation

`y=acosx+bsinx`

⟹ `dy/dx=−asinx+bcosx`

⟹ `d^2y/dx^2 =−acosx−bsinx`

⟹ `d^2y/dx^2 =−y`

⟹ `d^2y/dx^2+y=0`