The differential equation has equilibrium solutions at and

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

The differential equation

\dfrac{dy}{dx}=y(1-y)

has equilibrium solutions at

y=0

and

y=1

. Describe the long-term behavior, as

x

increases, of the solution curve that passes through

(0,\tfrac12)

. Toward which equilibrium solution, if any, does the curve move?