Professor Jason Levy, University of Ottawa, MAT 1332C, 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.
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1.
(a) Find the equilibrium solutions of the following differential equations.
You should find
three
y
0
=
y
3

6
y
2
+ 11
y

6
.
(b) Draw the phase line diagram.
(c) Graph the equilibrium solutions and sketch the solutions curves for the following initial
conditions:
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
→ ∞
.
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.
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 Winter '07
 MUNTEANU
 Exponential Function, World population, Mathematical constant, phase line diagram, Professor Jason Levy

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