The differential equation has equilibrium solutions at and
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
The differential equation dxdy=y2−4 has equilibrium solutions at y=−2 and y=2. Which statement best characterizes the long-term behavior of the solution curve that passes through (0,1) as x increases?
(a) The curve decreases without bound, moving toward y=−∞ as x increases.
(b) The curve rises and approaches the horizontal line y=2 as x increases.
(c) The curve decreases and approaches the horizontal line y=−2 without crossing it.
(d) The curve oscillates between y=−2 and y=2 because the slope alternates sign in that interval.