Apentix/AP Calculus AB/Unit 7: Differential Equations/Question
AP Calculus ABmediummcq1 pt

A student claims y=sin⁡xy = \sin x is a solution of y′′=−yy'' = -y. Is the claim correct?

A.Yes, because y′′=−sin⁡x=−yy'' = -\sin x = -y
B.Yes, because y′=−cos⁡xy' = -\cos x
C.No, because y′′=sin⁡xy'' = \sin x
D.No, because y′′=−cos⁡xy'' = -\cos x

Explanation

Core Concept

The first derivative is cos⁡x\cos x and the second derivative is −sin⁡x-\sin x, which equals −y-y.

Correct Answer

AYes, because y′′=−sin⁡x=−yy'' = -\sin x = -y

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