Explanation Given: The given differential equation is y ′ + y = 1 1 + e 2 t . Procedure used: For the first order differential equation y ′ + p ( t ) y = q ( t ) , the integrating factor is e ∫ p ( t ) d t . Then, the solution of the differential equation is y e ∫ p ( t ) d t = ∫ q ( t ) e ∫ p ( t ) d t d t . Calculation: Compare the given differential equation y ′ + y = 1 1 + e 2 t with the standard first order differential equation. Then, p ( t ) = 1 and q ( t ) = 1 1 + e 2 t . Calculate the integrating factor e ∫ p ( t ) d t as follows. e ∫ p ( t ) d t = e ∫ 1 d t = e t Substitute e t for e ∫ p ( t ) d t and 1 1 + e 2 t for q ( t ) in the solution y e ∫ p ( t ) d t = ∫ q ( t ) e ∫ p ( t ) d t d t for a differential equation

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Chapter 2.4, Problem 1E

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The solution of the differential equation.

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Chapter 2.3, Problem 28E

Chapter 2.4, Problem 2E

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Chapter 2 Solutions

Introductory Differential Equations

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