Q.1 a) Determine the equilibrium points of the autonomous equation (1) y(y - 3) 2 (Hint:...

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Q.1 a) Determine the equilibrium points of the autonomous equation (1) y(y - 3) 2 (Hint: the differential equation can be written in the form y = f(y) where f is a quadratic function.) b) Sketch a phase line plot and determine whether the critical points are asymptotically stable or unstable. c) Find an implicit equation that describes the corresponding integral curve y = y(t) with initial value y(0) = 3/2. d) Based on your finding, sketch the solution curve y = y(t). What is lim, y(t)? Q.1 a) Determine the equilibrium points of the autonomous equation (1) y(y - 3) 2 (Hint: the differential equation can be written in the form y = f(y) where f is a quadratic function.) b) Sketch a phase line plot and determine whether the critical points are asymptotically stable or unstable. c) Find an implicit equation that describes the corresponding integral curve y = y(t) with initial value y(0) = 3/2. d) Based on your finding, sketch the solution curve y = y(t). What is lim, y(t)?