Professor Robert Smith?, University of Ottawa, MAT 1332, Winter 2011 Assignment 4, due Monday March 7, 10:00am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Student Number DGD section By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Student Name 1. (a) Find the equilibrium solutions of the following diﬀerential equations. You should ﬁnd three y0 = y 3-6 y 2 + 11 y-6 . (b) Draw the phase line diagram. (c) Graph the equilibrium solutions and some other solutions. You should clearly indicate the behaviour of the solution curves as t → ∞ . 2. Suppose that size N if a populations satisﬁes the following diﬀerential equation: dN dt = 5 N 2 1 + N 2-2 N. (a) Find all equilibrium points. (b) Use the derivative criterion to decide if the equilibria are stable or unstable. (c) Draw the phase line diagram.
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