Explanation Given: The given system of differential equation is, d x d t = − 2 x + y d y d t = − 5 x + 4 y Procedure used: The phase plane equation for the system d x d t = f ( x , y ) and d y d t = g ( x , y ) is given by, d y d x = f ( x , y ) g ( x , y ) . Calculation: Consider the system of differential equation is, d x d t = − 2 x + y d y d t = − 5 x + 4 y The phase plane equation is, d y d x = − 5 x − 4 y − 2 x + y The direction field in the phase plane for the system is shown below

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 5.4, Problem 27E

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To sketch:

The direction field in phase plane for the system and predict the asymptotic limit (as t→+∞) of the solution starting at (1,1).

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Chapter 5.4, Problem 26E

Chapter 5.4, Problem 28E

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Fundamentals of Differential Equations and Boundary Value Problems

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The direction field in phase plane for the system and predict the asymptotic limit (as t → + ∞ ) of the solution starting at ( 1 , 1 ) .

Solution Summary: The author shows the direction field in phase plane for the system and predicts the asymptotic limit of the solution starting at (1,1).

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To sketch:

The direction field in phase plane for the system and predict the asymptotic limit (as t→+∞) of the solution starting at (1,1).

Want to see the full answer?

Chapter 5 Solutions

The direction field in phase plane for the system and predict the asymptotic limit (as t → + ∞ ) of the solution starting at ( 1 , 1 ) .

Solution Summary: The author shows the direction field in phase plane for the system and predicts the asymptotic limit of the solution starting at (1,1).

Concept explainers

Videos

To sketch: The direction field in phase plane for the system and predict the asymptotic limit (as t→+∞) of the solution starting at (1,1).

Want to see the full answer?

Chapter 5 Solutions

To sketch:

The direction field in phase plane for the system and predict the asymptotic limit (as t→+∞) of the solution starting at (1,1).