Question

If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:

• A. \( 8\sin x \cos x \)
• B. \( 3\sin x \cos x \)
• C. \( 1\)
• D. \(0 \)

Hint:

The second derivative test helps verify periodic functions.

Answer 1

The Correct Option is D

We know: \[ \frac{dy}{dx} = -5\sin x - 3\cos x,\]
\[\frac{d^2y}{dx^2} = -5\cos x + 3\sin x.
\] Adding \( y \): \[ \frac{d^2y}{dx^2} + y = (-5\cos x + 3\sin x) + (5\cos x - 3\sin x) = 0. \]