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Unformatted text preview: Assignment 4 Solutions 1. (a) Find the equilibrium solutions of the following differential equations. You should find three y prime = y 3 6 y 2 + 11 y 6 . (b) Draw the phase line diagram. Solution: We find the roots of f ( y ) = y 3 6 y 2 +11 y 6 = ( y 1)( y 2)( y 3) to be 1 , 2 , 3. Since f is a polynomial we easily identify the intervals where f is increasing/decreasing. This allows us to graph the phase line diagram: b 2 b 1 b 3 Of course, we an also use the derivative criterion to decide about stability. (c) Graph the equilibrium solutions and some solution curves 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 as t . Here are some graphs: y = 1 y = 2 y = 3 1 2 3 4 1 2 3 4 5 2. Suppose that size N if a populations satisfies the following differential equation: dN dt = 5 N 2 1 + N 2 2 N....
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This note was uploaded on 09/17/2011 for the course MAT 1332 taught by Professor Munteanu during the Winter '07 term at University of Ottawa.
 Winter '07
 MUNTEANU
 Equations

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