Sometimes a constant equilibrium solution has the property thatsolutions lying on one side of the equilibrium solution tend toapproach it, whereas solutions lying on the other side depart fromit. In this case the equilibrium solution is said to be semistable.Consider the equation dy/dt = y^2(4 − y 2 ) = f(y), where y(0) = y0and −∞ < y0 < ∞.
(i) Sketch the graph of f(y) versus y.
(ii) Determine the critical points. (iii) Classify each one asasymptotically stable, unstable, or semistable. (iv) Illustrateseveral solutions in the ty-plane that illustrate how the differentsolutions depend upon y0.
