Apentix/AP Calculus AB/Unit 7: Differential Equations/Question
AP Calculus ABhardmcq1 pt

Which of the following is the general solution of dydx=cos⁡x y\dfrac{dy}{dx} = \cos x\, y?

A.y=Cesin⁡xy = Ce^{\sin x}
B.y=Csin⁡xy = C\sin x
C.y=Cecos⁡xy = Ce^{\cos x}
D.y=Ccos⁡xy = C\cos x

Explanation

Core Concept

Separating variables gives ln⁡∣y∣=sin⁡x+C\ln|y| = \sin x + C, so exponentiating yields y=Cesin⁡xy = Ce^{\sin x}.

Correct Answer

Ay=Cesin⁡xy = Ce^{\sin x}

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