Explanation Procedure used: If the differential equation has no critical points then there does not exist a value y such that f ( y ) = 0 . So, the differential equation has no constant solutions. Calculation: Consider the autonomous differential equation. d y d x = f ( y ) The above autonomous differential equation has no critical points. So, the differential equation has no constant solutions. y ( x ) = c The solution y ( x ) will not be bounded above or below

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Chapter 2.1, Problem 37E

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To discuss: The behavior of the solutions having no critical points.

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Chapter 2.1, Problem 36E

Chapter 2.1, Problem 38E

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Chapter 2 Solutions

EBK ADVANCED ENGINEERING MATHEMATICS

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The behavior of the solutions having no critical points.

Solution Summary: The author explains the behavior of the solutions having no critical points, which is the case in that the solution assumes all real values.

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Chapter 2 Solutions