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The direction field for is shown in dy/dx = 4x/y Figure

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 2E Chapter 1.3

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 2E

Problem

The direction field for is shown in dy/dx = 4x/y Figure 1.13.

(a) Verify that the straight lines y = ± 2x are solution curves, provided x ≠ 0.

(b) Sketch the solution curve with initial condition y (0) = 2.

(c) Sketch the solution curve with initial condition y(2) = 1.

(d) What can you say about the behavior of the above solutions as x + ∞? How about - ∞

Step-by-Step Solution:

Step 1 ;

In this problem given that

 

Consider

Given that the straight lines

 

 is verified.

Then the below graph shows the solution equation .

Step 2 :

(b)

Solve for

.’.

Using the initial condition

The direction formula of the graph is

Step 3 :

(c)

Using the initial condition

.’.

The graph is

Step 5 :

(d)

Below graph shows the and

Hence the result.

Step 4 of 5

Chapter 1.3, Problem 2E is Solved
Step 5 of 5

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

The answer to “The direction field for is shown in dy/dx = 4x/y Figure 1.13.(a) Verify that the straight lines y = ± 2x are solution curves, provided x ? 0.(b) Sketch the solution curve with initial condition y (0) = 2.(c) Sketch the solution curve with initial condition y(2) = 1.(d) What can you say about the behavior of the above solutions as x + ?? How about - ?” is broken down into a number of easy to follow steps, and 68 words. Since the solution to 2E from 1.3 chapter was answered, more than 705 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This full solution covers the following key subjects: solution, curve, condition, initial, Lines. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The full step-by-step solution to problem: 2E from chapter: 1.3 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM.

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The direction field for is shown in dy/dx = 4x/y Figure

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