(a) Show that if depends only on the product xy, that is,

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

Problem 15E Chapter 2.5

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 15E

(a) Show that if  depends only on the product xy, that is,

then the equation  has an integrating factor of the form µ (xy) Give the general formula for µ (xy).

(b) Use your answer to part (a) to find an implicit solution to

satisfying the initial condition y (1) = 1.

Step-by-Step Solution:

Step 1 :

In this problem we have to find the integrating factor.

Consider

and also given that  

Let be an integrating factor

Multiplying in equation (1)

This equation exact

Step 2 :

Then

Then

Step 3 :

.’.

This is the general form of the integrating factor.

Step 4 of 5

Chapter 2.5, Problem 15E is Solved
Step 5 of 5

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

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