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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider
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In 19–24, convert the given second-order

Chapter 5, Problem 21E

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QUESTION:

In 19–24, convert the given second-order equation into a first-order system by setting . Then find all the critical points in the -plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12). Figure 5.12 Examples of different trajectory behaviors near critical point at origin

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QUESTION:

In 19–24, convert the given second-order equation into a first-order system by setting . Then find all the critical points in the -plane. Finally, sketch (by hand or software) the direction fields, and describe the stability of the critical points (i.e., compare with Figure 5.12). Figure 5.12 Examples of different trajectory behaviors near critical point at origin

ANSWER:

SolutionStep 1In this problem, we have to convert the second order to first order differential equation by setting and also we have to find the critical points in the plane.

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