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# (a) Show that if depends only on the product xy, that is, ISBN: 9780321747730 43

## Solution for problem 15E Chapter 2.5

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

Step 5 of 5

##### ISBN: 9780321747730

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