After solving the differential equation

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

Problem

\dfrac{dy}{dx}=y^2-9

, a student arrives at the relation

\ln\left|\dfrac{y-3}{y+3}\right| = 2x + C

. Which of the following is an equivalent explicit expression for the general solution

y(x)

valid on any interval where

y \neq \pm 3

? (a)

\displaystyle y = \dfrac{3}{1-Ce^{2x}}

(b)

\displaystyle y = 3\,\tanh(3x+C)

(c)

y = 3\,\dfrac{1+Ce^{2x}}{1-Ce^{2x}}

(d)

y = 3Ce^{2x}