Professor Jason Levy, University of Ottawa, MAT 1332C, Winter 2011Assignment 4, due Monday March 7, 10:00am at the beginning of class.Late assignments will not be accepted; nor will unstapled assignments.Student NumberDGD sectionBy signing below, you declare that this work was your own and that you have not copied from anyother individual or other source.SignatureStudent Name1.(a) Find the equilibrium solutions of the following differential equations.You should findthreey0=y3-6y2+ 11y-6.(b) Draw the phase line diagram.(c) Graph the equilibrium solutions and sketch the solutions curves for the following initialconditions:y(0) = 0, y(0) = 0.5, y(0) = 1.5, y(0) = 2.5, y(0) = 4.You should clearly indicate the behaviour of the solution curves ast→ ∞.2. Suppose that sizeNif a populations satisfies the following differential equation:dNdt=5N21 +N2-2N.(a) Find all equilibrium points.(b) Use the derivative criterion to decide if the equilibria are stable or unstable.
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