Explanation Formula used: a) Formula for linear differential equation is, d y d x + P ( x ) y = Q ( x ) b) Integrating factor for the linear differential equation is, μ ( x ) = e ∫ P ( x ) d x c) Formula of integration by part is as follows, ∫ u v d x = u ( ∫ v d x ) − ∫ { d u d v ∫ v d x } d x Calculation: Consider the given equation, d y d x = x 2 e − 4 x − 4 y Rearrange the equation d y d x = x 2 e − 4 x − 4 y as follows, d y d x = x 2 e − 4 x − 4 y d y d x + 4 y = x 2 e − 4 x …… ( 1 ) Compare the above equation with the linear differential equation as follows, Here, P ( x ) = 4 and Q ( x ) = x 2 e − 4 x Find the integrating factor for the equation ( 1 ) as follows,

Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

7th Edition

ISBN: 9780321977182

Author: Nagle, R. Kent, Saff, Edward B., Snider, Arthur David

Publisher: PEARSON

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Chapter 2.3, Problem 12E

To determine

To find:

The general solution of the equation dydx=x2e−4x−4y.

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Chapter 2.3, Problem 11E

Chapter 2.3, Problem 13E

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Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

Ch. 2.2 - Prob. 1E Ch. 2.2 - In Problems 1-6, determine whether the given...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E

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