Explanation Given: The given equation is y ′ + y = cos t + sin t . Procedure used: The standard form of the given equation is y ′ + P ( t ) y = Q ( t ) . The integrating factor is calculated as e ∫ P ( t ) d t . To find the general solution, multiply by the integrating factor, apply the theorem, integrate and solve for y . Calculation: Rewrite the given equation in the standard form. d y d t + y = cos t + sin t Here, P ( t ) = 1 . Thus, the integrating factor is calculated as, e ∫ P ( t ) d t = e ∫ d t = e t That is, the integrating factor is μ ( t ) = e t . Multiply throughout by the integrating factor and integrate to solve for y as follows

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Chapter 2.3, Problem 6E

To determine

The solution of the given differential equation.

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Chapter 2.3, Problem 5E

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Chapter 2 Solutions

Introductory Differential Equations

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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