The differential equation for which $y=a \cos x+b \sin x$ is a solution, is
Answer & explanation
Correct answer: option 1
We have,
$y=a \cos x+b \sin x$
$\Rightarrow \frac{d y}{d x}=-a \sin x+b \cos x$
$\Rightarrow \frac{d^2 y}{d x^2}=-a \cos x-b \sin x \Rightarrow \frac{d^2 y}{d x^2}=-y$