The differential equation depends on the real parameter

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

Problem

The differential equation

\displaystyle \frac{dy}{dx}=k y-y^{3}

depends on the real parameter

k

. A slope field is said to have exactly three distinct horizontal lines when the equation has three distinct real equilibrium values of

y

. For which of the following values of

k

does the slope field have exactly three distinct horizontal lines? (a)

k=-4

(b)

k=0

(c)

k=3

(d)

k=-9