a. Consider the equation dy = k(1 – y)? where k is a positive constant. Show that y = 1 is the only critical point, with the corresponding equilibrium solution dt) = 1. b. Sketch ly) versus y. Show that y is increasing as a function of t for y< 1 and also for y > 1. The phase line has upward-pointing arrows both below and above y = 1. Thus solutions below the equilibrium solution approach it, and those above it grow farther away. Therefore, ɖt) = 1 is semistable. c. Solve the equation subject to the initial condition y(0) = yo and confirm the conclusions reached in part b.