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# Solution: In 19–24, convert the given second-order equation ISBN: 9780321747730 43

## Solution for problem 23E Chapter 5.4

Fundamentals of Differential Equations | 8th Edition

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Problem 23E

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

Step-by-Step Solution:

Solution : Step 1 of 4 : In this problem, we need to convert the given second-order equation into a first-order system by setting and find the critical points, then sketch the direction fields, and describe the stability of the critical points.Step 2 of 4 : Given system of equation is y’’ + y - = 0v = Differentiate itv’ = y’’ y’’ = -y + v’ = - y

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The full step-by-step solution to problem: 23E from chapter: 5.4 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 23E from 5.4 chapter was answered, more than 244 students have viewed the full step-by-step answer. The answer to “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” is broken down into a number of easy to follow steps, and 57 words. This full solution covers the following key subjects: critical, order, points, figure, hand. This expansive textbook survival guide covers 67 chapters, and 2118 solutions.

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