4th Edition

ISBN: 9780495561989

Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall

Publisher: Cengage Learning

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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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Textbook Question

Chapter 2.2, Problem 8E

Convert the second-order differential equation
1 d 2 y d t 2 + 2 y = 0
into a first-order system in terms of y and v where v = dy/dt.
(a) Determine the vector field associated with the first-order system.
(b) Sketch enough vectors in the vector field to get a sense of its geometric structure. (You should do this part of the exercise without the use of technology.)
(c) Use HPGSystemSolver to sketch the associated direction field.
(d) Make a rough sketch of the phase portrait of the system and confirm your answer using HPGSystemsolver.
(e) Briefly describe the behavior of the solutions.

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Chapter 2.2, Problem 7E

Chapter 2.2, Problem 9E

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Chapter 2 Solutions

Differential Equations

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Solution Summary: The author explains how to calculate the vector field associated with the given first-order system.

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