The autonomous differential equation

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

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

, where

k

is a positive real parameter, has two equilibrium solutions

y=0

and

y=k

. For which values of

k

is the equilibrium solution

y=0

stable? Justify your answer briefly.