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AP® Calculus AB-BC

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Separation of Variables: Family of Solutions

APCALC-79D$F9

Which of the following could be a solution to the differential equation $\cfrac{dy}{dx} = \cfrac {\cos {x}}{y}$?

I. $y=-\sqrt{2\sin{x}}$
II. $y=-\sqrt{2\sin{x} +\pi}$
III. $y=\pi -\sqrt{2\sin{x}}$

A

I only

B

II only

C

I and II only

D

I and III only