Question:
If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:
If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:
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The second derivative test helps verify periodic functions.
Updated On: Mar 28, 2026
- \( 8\sin x \cos x \)
- \( 3\sin x \cos x \)
- \( 1\)
- \(0 \)
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The Correct Option is D
Solution and Explanation
We know:
\[
\frac{dy}{dx} = -5\sin x - 3\cos x,\]
\[\frac{d^2y}{dx^2} = -5\cos x + 3\sin x.
\] Adding \( y \): \[ \frac{d^2y}{dx^2} + y = (-5\cos x + 3\sin x) + (5\cos x - 3\sin x) = 0. \]
\[\frac{d^2y}{dx^2} = -5\cos x + 3\sin x.
\] Adding \( y \): \[ \frac{d^2y}{dx^2} + y = (-5\cos x + 3\sin x) + (5\cos x - 3\sin x) = 0. \]
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