Explanation Given information: The differential equation y ' = k ( y − A ) , where k < 0 and A > 0 Graph: The zero of the graph g ( y ) = k ( y − A ) is y = A . By using the property of an autonomous differential equation: Each zero of g ( y ) , there is a constant solution of the differential equation. Specifically, if g ( c ) = 0 , the constant function y = c is a solution. Thus, the differential equation g ( y ) = k ( y − A ) has a constant solution at y = A . The graph of the function z = g ( y ) = k ( y − A ) on a y z -coordinate system and the graph of the constant solution on t y - coordinate system is shown in Fig. (a) and Fig. (b) below:

15th Edition

ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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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 10.5, Problem 36E

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To graph: The differential equation y' = k(y−A), where k< 0 and A > 0. Using the qualitative theory of the autonomous differential equations; also, include a yz-graph, if one is not already provided and indicate the constant solutions on ty-graph.

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Chapter 10.5, Problem 35E

Chapter 10.5, Problem 37E

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To graph: The differential equation y ' = k ( y − A ) , where k < 0 and A > 0 . Using the qualitative theory of the autonomous differential equations; also, include a y z -graph, if one is not already provided and indicate the constant solutions on t y -graph.

Solution Summary: The author illustrates the qualitative theory of the autonomous differential equations by using a yz -graph, if one is not already provided.

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To graph: The differential equation y' = k(y−A), where k< 0 and A > 0. Using the qualitative theory of the autonomous differential equations; also, include a yz-graph, if one is not already provided and indicate the constant solutions on ty-graph.

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Chapter 10 Solutions

To graph: The differential equation y ' = k ( y − A ) , where k &lt; 0 and A &gt; 0 . Using the qualitative theory of the autonomous differential equations; also, include a y z -graph, if one is not already provided and indicate the constant solutions on t y -graph.

Solution Summary: The author illustrates the qualitative theory of the autonomous differential equations by using a yz -graph, if one is not already provided.

Concept explainers

Videos

To graph: The differential equation y' = k(y−A), where k< 0 and A > 0. Using the qualitative theory of the autonomous differential equations; also, include a yz-graph, if one is not already provided and indicate the constant solutions on ty-graph.

Want to see the full answer?

Chapter 10 Solutions

To graph: The differential equation y ' = k ( y − A ) , where k < 0 and A > 0 . Using the qualitative theory of the autonomous differential equations; also, include a y z -graph, if one is not already provided and indicate the constant solutions on t y -graph.