To draw: The direction field and describe it’s behavior.

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Answer 1

Question

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

Answer 2

Question

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Answer 6

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

Answer 7

Chapter 9.5, Problem 2P

(a)

To determine

To draw: The direction field and describe it’s behavior.

Answer 8

(b)

To determine

The critical point.

Answer 9

(b)

To determine

The critical point.

Answer 10

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

Answer 11

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

Answer 12

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

Answer 13

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

Answer 14

(e)

To determine

To draw: A phase portrait of given differential system.

Answer 15

(e)

To determine

To draw: A phase portrait of given differential system.

Answer 16

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Answer 17

(f)

To determine

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P

To draw: The direction field and describe it’s behavior.

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To draw: The direction field and describe it’s behavior.

The critical point.

The corresponding linear system, eigen value and eigen vector at each critical point.

To sketch: The trajectories in the neighborhood of each critical point.

To draw: A phase portrait of given differential system.

The limiting behavior of x and y as t→∞ and interpret the results in terms of the populations of the two species.

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Chapter 9 Solutions