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In 1–8, classify the equation as separable, | Ch 2.4 - 8E

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

Problem 8E Chapter 2.4

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 8E

In 1–8, classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

Step-by-Step Solution:

SOLUTIONStep 1We have to check the given differential equation is separable, linear or exact.Step 2First we check given equation is linear or not.We have, a first order linear equation is of the form,Step 3Given differential equation is Which is of the form where and Therefore it is linear.Step 4Next we have to check it is separable or not.Step 5If the given differential equation is separable, then it can be written as f()d = g(y)dyStep 6.Given differential equation is This can not be expressed is of the form, f()d = g(y)dy.Therefore this is not separable.Step 7Next we have to check the given differential equation is exact or not.We have, a differential equation M dx+N dy is exact if and only if Step 8Given equation is Here and Find =1=3Here Therefore the given differential equation is not exact.Step 9We conclude that the given differential equation, is linear is not separable and is not exact.

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Chapter 2.4, Problem 8E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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In 1–8, classify the equation as separable, | Ch 2.4 - 8E

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