a. Explanation Given information : the differential equation is y ' = x cos π y . Graph : From the direction field provided in the question it can be observed that, The solution of differential equation is ln | s e x π y + tan π y | = π x 2 2 + c . So now for the initial conditions, change the y -intercept of the solution of the differential equation, Substitute c by 0 , 1 , 0.5 , 1.6 . All the solutions are equilibrium solutions, so use plotting approach to make graph, x 0 0 0 0 y 0 1 0.5 1.6 The graph is obtained as: Interpretation : from the above graph it can be observed that the graph of all initial conditions are y -intercept change. b. To determine To find : the all equilibrium solutions. Answer The solution is ln | s e x π y · tan π y | = π x 2 2 Explanation Given information : the differential equation is y ' = x cos π y . Calculation : from the above part , It can be observed that for the given initial conditions the differential equation has equilibrium solutions. Thus, the solutions is ln | s e x π y · tan π y | = π x 2 2

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

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ISBN: 9781337687805

Author: James Stewart

Publisher: Cengage Learning

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Differential Equations

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Question

Chapter 7.2, Problem 1E

To determine

To graph : the solutions that satisfy the initial conditions.

Expert Solution

Explanation of Solution

Given information :

the differential equation is y'=xcosπy .

Graph :

From the direction field provided in the question it can be observed that,

The solution of differential equation is ln|sexπy+tanπy|=πx22+c .

So now for the initial conditions, change the y -intercept of the solution of the differential equation,

Substitute c by 0,1,0.5,1.6 .

All the solutions are equilibrium solutions, so use plotting approach to make graph,

x	0	0	0	0
y	0	1	0.5	1.6

The graph is obtained as:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 7.2, Problem 1E

Interpretation : from the above graph it can be observed that the graph of all initial conditions are y -intercept change.

To determine

To find : the all equilibrium solutions.

Expert Solution

Answer to Problem 1E

The solution is ln|sexπy·tanπy|=πx22

Explanation of Solution

Given information :

the differential equation is y'=xcosπy .

Calculation : from the above part ,

It can be observed that for the given initial conditions the differential equation has equilibrium solutions.

Thus, the solutions is ln|sexπy·tanπy|=πx22

Chapter 7.1, Problem 15E

Chapter 7.2, Problem 2E

Chapter 7 Solutions

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - Prob. 4E Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Prob. 9E Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.5 - Prob. 1E Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Prob. 4E Ch. 7.5 - Prob. 5E Ch. 7.5 - Prob. 6E Ch. 7.5 - Prob. 7E Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7 - Prob. 1RCC Ch. 7 - Prob. 2RCC Ch. 7 - Prob. 3RCC Ch. 7 - Prob. 4RCC Ch. 7 - Prob. 5RCC Ch. 7 - Prob. 6RCC Ch. 7 - Prob. 7RCC Ch. 7 - Prob. 8RCC Ch. 7 - Prob. 1RQ Ch. 7 - Prob. 2RQ Ch. 7 - Prob. 3RQ Ch. 7 - Prob. 4RQ Ch. 7 - Prob. 5RQ Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 1P Ch. 7 - Prob. 2P Ch. 7 - Prob. 3P Ch. 7 - Prob. 4P Ch. 7 - Prob. 5P Ch. 7 - Prob. 6P Ch. 7 - Prob. 7P Ch. 7 - Prob. 8P Ch. 7 - Prob. 9P Ch. 7 - Prob. 10P Ch. 7 - Prob. 11P Ch. 7 - Prob. 12P Ch. 7 - Prob. 13P Ch. 7 - Prob. 14P

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