Consider the differential equation

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Consider the differential equation

\displaystyle \frac{dy}{dx}=\frac{x\cos x}{1+e^{y}}

. Which of the following implicit relations is a correct general solution? (a)

e^{y}-y=x\sin x+\cos x+C

(b)

y+e^{y}=x\sin x-\cos x+C

(c)

y+e^{y}=x\sin x+\cos x+C

(d)

e^{y}+y=\sin x+x\cos x+C

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