For the differential equation

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

Problem

\dfrac{dy}{dx}=(y-2)(y+1)

, consider the solution curve passing through

(0,0)

. Describe its long-term behavior by identifying which equilibrium solution it approaches as

x\to\infty

and which equilibrium it approaches as

x\to-\infty