The differential equation for which $y=a\, cos \, x + b \, sin \, x $ is a solution, is
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $\frac{d^y}{dx^2}+y = 0 $
We have,
$y=acosx + b sin x$
$⇒\frac{dy}{dx}= - a sin x + b \, cos x$
$⇒\frac{d^2y}{dx^2}=-acos x - b sin x $
$⇒\frac{d^2y }{dx^2}=-y $