Question 4 (20% or 30 minutes) a) (10 points) Consider the following non linear differential equation: y = -2(12 -1)e-0.5t Assume that y(0) = 100, find the solution. What type of convergence do we have here? b) (5 points) Consider the following nonlinear differential equation: y = y(y -10)(y -20) Draw the phase diagram, identify each steady state an explain whether they are stable or unstable. c) (5 points) Consider the following non linear difference equation: Yi+1 = (3Y, - 2)0.5 Draw the phase diagram, identify each steady state an explain whether they are stable or unstable