Show that the linearization of the system in (8) at .3; 0/

Differential Equations and Boundary Value Problems: Computing and Modeling | 5th Edition | ISBN: 9780321796981 | Authors: C. Henry Edwards, David E. Penney, David T. Calvis

Problem 21 Chapter 6.3

Differential Equations and Boundary Value Problems: Computing and Modeling | 5th Edition

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Differential Equations and Boundary Value Problems: Computing and Modeling | 5th Edition | ISBN: 9780321796981 | Authors: C. Henry Edwards, David E. Penney, David T. Calvis

Differential Equations and Boundary Value Problems: Computing and Modeling | 5th Edition

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Problem 21

Show that the linearization of the system in (8) at .3; 0/ is u0 D 3u 3v, v0 D 2v. Then show that the coefficient matrix of this linear system has the positive eigenvalue 1 D 3 and the negative eigenvalue 2 D 2. Hence .3; 0/ is a saddle point for (8). 2

Step-by-Step Solution:
Step 1 of 3

L20 - 3 dy 2 3 ex. Now we can find if x y − 4x = y . dx 2 2 ex. Find the sl√pe...

Step 2 of 3

Chapter 6.3, Problem 21 is Solved
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Textbook: Differential Equations and Boundary Value Problems: Computing and Modeling
Edition: 5
Author: C. Henry Edwards, David E. Penney, David T. Calvis
ISBN: 9780321796981

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Show that the linearization of the system in (8) at .3; 0/

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