If y = f(x) is solution of a differential equation then differentiating y = f(x) will give the same differential equation

Let us find the differential equation by differentiating y with respect to x twice

Why twice because all the options have order as 2 and also because there are two constants A and B

y = e^-x (A cos x + B sin x)

Differentiating using product rule

But e^-x (A cos x + B sin x) = y

Differentiating again with respect to x

But e^-x (A cos x + B sin x) = y

Also which means