# If y = e-x (A cos x + B sin x), then y is a solution ofA. B. C. D.

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

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