If $y=A \sin x+B \cos x$, then which of

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

If $y=A \sin x+B \cos x$, then which of the following is correct?

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (2) → $\frac{d^2 y}{d x^2}+y=0$

$y=A\sin x+B\cos x$ ...(1)

$⇒\frac{dy}{dx}=A\cos x-B\sin x$

$⇒\frac{d^2y}{dx^2}=-A\sin x-B\cos x$ ...(2)

∴ from (1) and (2),

$⇒\frac{d^2y}{dx^2}+y=0$