If y = e–x (A cos x + B sin x),

Question:

If ex (A cos + B sin x), then is a solution of

(A) $\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}=0$

(B) $\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0$

(C) $\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+2 y=0$

(D) $\frac{d^{2} y}{d x^{2}}+2 y=0$

 

Solution:

Correct option is (C).

Given equation, ex (A cos + B sin x)

Differentiating on both the sides, w.r.t. x, we get

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