For the differential equation

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

Problem

\dfrac{dy}{dt}=y(2-y)

, which statement correctly classifies the stability of each equilibrium solution? (a) The equilibria

y=0

and

y=2

are both stable. (b) The equilibrium

y=0

is stable, and

y=2

is unstable. (c) The equilibrium

y=0

is unstable, and

y=2

is stable. (d) The equilibrium

y=0

is semistable, and

y=2

is unstable.