1. An equilibrium solution y = c is called asymptotically stable (or attracting) if all nearby solutions converge to c. More precisely, there is an interval (a,b) containing c, such that for every co in (a,b), the solution y = f(x) to the initial-value problem y(0) = co has limg oo f(@) = 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 five ways the y' = F'(y) curve might look (at an equilibrium) near the y-axis: A B Cc D E In which of these five cases will the equilibrium solutions be asymptotically stable? Hint: Draw nearby direction fields and plot representative solution curves