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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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Solution: In 15–18, find all critical points for the given

Chapter 5, Problem 17E

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QUESTION:

In Problems 15-18. find all critical points for the given system. Then use a software package to sketch the direction field in the phase plane and from this describe the stability of the critical points (i.e., compare with Figure 5.12).

                                                     \(\frac{d x}{d t}=2 x+13 y\),

                                                            \(\frac{d y}{d t}=-x-2 y\)

Equation transcription:

Text transcription:

\frac{d x}{d t}=2 x+13 y

\frac{d y}{d t}=-x-2 y

Questions & Answers

QUESTION:

In Problems 15-18. find all critical points for the given system. Then use a software package to sketch the direction field in the phase plane and from this describe the stability of the critical points (i.e., compare with Figure 5.12).

                                                     \(\frac{d x}{d t}=2 x+13 y\),

                                                            \(\frac{d y}{d t}=-x-2 y\)

Equation transcription:

Text transcription:

\frac{d x}{d t}=2 x+13 y

\frac{d y}{d t}=-x-2 y

ANSWER:

SOLUTION
Step 1

Given system is

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