Explanation Formula used: Formula for linear differential equation is, d y d x + P ( x ) y = Q ( x ) Integrating factor for the linear differential equation is, μ ( x ) = e ∫ P ( x ) d x Calculation: Consider the given equation, x d y d x + 2 y = x − 3 Rearrange the equation x d y d x + 2 y = x − 3 as follows, x d y d x + 2 y = x − 3 d y d x + 2 x y = x − 4 …… ( 1 ) Compare the above equation with the linear differential equation as follows, Here, P ( x ) = 2 x and Q ( x ) = x − 4 Find the integrating factor for the equation ( 1 ) as follows, μ ( x ) = e ∫ 2 x d x = e 2 ln | x | = x 2 Multiply with x 2 in equation ( 1 ) and find the required solution,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 2.3, Problem 10E

To determine

To find:

The general solution of the equation xdydx+2y=x−3.

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Chapter 2.3, Problem 9E

Chapter 2.3, Problem 11E

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Fundamentals of Differential Equations and Boundary Value Problems

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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