The differential equation dtdy=y3−4y has equilibrium solutions at y=−2, y=0, and y=2.
Which statement most accurately describes the stability of these equilibria and the long-term behavior of a solution satisfying y(0)=1?
a) y=−2 and y=0 are unstable, y=2 is stable, and the solution with y(0)=1 approaches y=2 as t→∞.
b) y=−2 and y=2 are unstable, y=0 is stable, and the solution with y(0)=1 approaches y=0 as t→∞.
c) y=−2 and y=2 are stable, y=0 is unstable, and the solution with y(0)=1 approaches y=2 as t→∞.
d) y=−2 is stable, y=0 and y=2 are unstable, and the solution with y(0)=1 approaches y=−2 as t→∞.