Mathematics

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

k=0

k=3

k=-9