1. An equilibrium solution 3; = c is called asymptotically stable (or attracting) if all nearby solutions converge to c. More precisely, there is an interval (a, b) containing 0, such that for every (:0 in (a, b), the solution y = f (1c) to the initialvalue problem y(0) = on has limmam f (:0) = 0 Remark: Think about this like a ball at the bottom of a valley. If we push it a little, it will still return to the bottom after rocking back and forth. There are ve ways the y' = F(y) curve might look (at an equilibrium) near the yaxis: A n C o E In which of these ve cases will the equilibrium solutions be asymptotically stable? Hint: Draw nearby direction elds and plot representative solution curves