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As stated in this section, the separation of equation (2)

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

Solution for problem 30E Chapter 2.2

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 30E

As stated in this section, the separation of equation (2) on page 39 requires division by p(y), and this may disguise the fact that the roots of the equation p(y) = 0 are actually constant solutions to the differential equation.

(a) To explore this further, separate the equation

to derive the solution,

y = -1 + (x2/6 - x + C)3.

(b) Show that y = -1 satisfies the original equation dy/dx = (x-3)(y+1).

(c) Show that there is no choice of the constant C that will make the solution in part (a) yield the solution y = -1. Thus, we lost the solution y = -1 when we divided by (y+1)2/3.

Step-by-Step Solution:

Solution:

Step 1

(a). In this problem we have to derive solution  from the differential equation

.

We have differential equation

Using method of ‘separating variable’

We get,

On integrating both side,

Or, .

Or,

Or,

Or, .

Hence, solution   is derived from the differential equation

.

Step 2 of 3

Chapter 2.2, Problem 30E is Solved
Step 3 of 3

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

The full step-by-step solution to problem: 30E from chapter: 2.2 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 30E from 2.2 chapter was answered, more than 362 students have viewed the full step-by-step answer. The answer to “?As stated in this section, the separation of equation (2) on page 39 requires division by p(y), and this may disguise the fact that the roots of the equation p(y) = 0 are actually constant solutions to the differential equation.(a) To explore this further, separate the equationto derive the solution,y = -1 + (x2/6 - x + C)3.(b) Show that y = -1 satisfies the original equation dy/dx = (x-3)(y+1)?.(c) Show that there is no choice of the constant C that will make the solution in part (a) yield the solution y = -1. Thus, we lost the solution y = -1 when we divided by (y+1)2/3.” is broken down into a number of easy to follow steps, and 107 words. This full solution covers the following key subjects: equation, solution, constant, may, disguise. This expansive textbook survival guide covers 67 chapters, and 2118 solutions.

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As stated in this section, the separation of equation (2)