Explanation Given: The given differential equation is, d y d x = ( 2 π ) y − sin y . Calculation: Consider the given differential equation as function of y . f ( y ) = ( 2 π ) y − sin y Substitute 0 for f ( y ) in the above equation. ( 2 π ) y − sin y = 0 ( 2 π ) y = sin y The critical points of the differential equation are the intersection points of the two curves y 1 = ( 2 π ) y and y 2 = sin y . The graph of equations are shown below in Figure 1. From above Figure 1, it can be easily analyzed that the given equation has only three solutions which are the intersection points, − π 2 , 0 , π 2 . The critical points of the differential equation are − π 2 , 0 , π 2 . Consider the Figure 1

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.1, Problem 31E

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To find: The critical points of the given differential equation, obtain a phase portrait and classify the critical points.

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Chapter 2.1, Problem 30E

Chapter 2.1, Problem 32E

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Chapter 2 Solutions

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The critical points of the given differential equation, obtain a phase portrait and classify the critical points.

Solution Summary: The author analyzes the critical points of the given differential equation by obtaining a phase portrait and classifying them.

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To find: The critical points of the given differential equation, obtain a phase portrait and classify the critical points.

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Chapter 2 Solutions