Consider the differential equation

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

Problem

\dfrac{dy}{dt}=y(y+1)(y-3)

. The equation has equilibrium solutions at

y=-1

and

y=3

. Which of the following correctly classifies the stability of these two equilibria, in the order

y=-1

then

y=3

? (a) Stable, unstable (b) Unstable, semi-stable (c) Unstable, unstable (d) Unstable, stable