Mathematics

Problem

For the differential equation

\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.