If $y=5 \cos x-3 \sin x$, then $\frac{d^2 y}{d x^2}+y$ is equal to
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If $y=5 \cos x-3 \sin x$, then $\frac{d^2 y}{d x^2}+y$ is equal to

(A) -1

(B) 2

(C) 1

(D) 0

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Best answer

SOLUTION —

$y=5 \cos x-3 \sin x$

$\begin{array}{l}\Rightarrow \quad \frac{d y}{d x}=-5 \sin x-3 \cos x \\\Rightarrow \quad \frac{d^2 y}{d x^2}=-5 \cos x+3 \sin x \\\therefore \quad \frac{d^2 y}{d x^2}+y=-5 \cos x+3 \sin x+5 \cos x-3 \sin x=0\end{array}$

So, The correct option will be (D).

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