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AP® Calculus AB-BC

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Separation of Variables III

APCALC-1A3F$S

If the graph of $y=f(x)$ passes through the point $(-1, \, -2)$ and $\cfrac{dy}{dx} = \cfrac{7}{2y \cdot (x + 2)}$ for all $x \ge -1$, then $y(x)=$

A

$y = \pm \sqrt {7\ln \left| {x + 2} \right| + 4} $; $x \ge -1$

B

$y =-2 - \sqrt {7\ln \left| {x + 2} \right| } $; $x \ge -1$

C

$y =-2 \pm \sqrt {7\ln \left| {x + 2} \right| } $; $x \ge -1$

D

$y = - \sqrt {7\ln \left| {x + 2} \right| + 4} $; $x \ge -1$