The differential equation for which $y = a\cos x + b\sin x$ is a

Given that, $y = a\cos x + b\sin x$

On differentiating both sides w.r.t. $x$,

we get

$\frac{{dy}}{{dx}} = - a\sin x + b\cos x$

Again, differentiating w.r.t. $x$,

we get
$\frac{{{d^2}y}}{{d{x^2}}} = - a\sin x + b\cos x$

$\Rightarrow$ $\frac{{{d^2}y}}{{d{x^2}}} = - y$

$\Rightarrow$ $\frac{{{d^2}y}}{{d{x^2}}} + y = 0$