Explanation Given: The given differential equation is d y d t − 2 t ( 1 + t 2 ) y = 2 . Procedure used: For the first order differential equation y ′ + p ( t ) y = q ( t ) , calculate integrating factor e ∫ p ( t ) d t and then the solution of the differential equation is given by y e ∫ p ( t ) d t = ∫ q ( t ) e ∫ p ( t ) d t d t . Calculation: Consider the given Differential equation. d y d t − 2 t ( 1 + t 2 ) y = 2 Compare the above equation with standard first order differential equation. p ( t ) = − 2 t ( 1 + t 2 ) , and q ( t ) = 2 . Calculate the integrating factor e ∫ p ( t ) d t . e ∫ p ( t ) d t = e ∫ − 2 t ( 1 + t 2 ) d t = e − ln ( 1 + t 2 ) = 1 ( 1 + t 2 ) Now, the solution of the given differential equation is given by, y e ∫ p ( t ) d t = ∫ q ( t ) e ∫ p ( t ) d t d t Substitute 1 ( 1 + t 2 ) for e ∫ p ( t ) d t and 2 for q ( t )

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Differential Equations

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Chapter 2.4, Problem 10E

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The solution of the differential equation dydt−2t(1+t2)y=2.

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Chapter 2.4, Problem 9E

Chapter 2.4, Problem 11E

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Chapter 2 Solutions

Introductory Differential Equations

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The solution of the differential equation d y d t − 2 t ( 1 + t 2 ) y = 2 .

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The solution of the differential equation dydt−2t(1+t2)y=2.

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Chapter 2 Solutions