For the differential equation

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

Problem

\dfrac{dy}{dt}=y^{2}-4

, which option correctly lists all equilibrium solutions and describes their stability? (a)

y=-2

and

y=2

; both are stable because nearby solutions move toward them from either side. (b)

y=-2

is stable, and

y=2

is unstable. These are the only equilibrium solutions. (c)

y=-2

and

y=2

; both are unstable because nearby solutions move away from them on either side. (d)

y=-2

is unstable, and

y=2

is stable. These are the only equilibrium solutions.