Explanation Procedure used: The standard form of the linear differential equation: d y d x + P ( x ) y = f ( x ) The integrating factor for above equation is e ∫ P ( x ) d x . The product rule of integrals is ∫ u d v = u v − ∫ v d u . Calculation: Consider the given differential equation. x d y d x + 2 y = 3 Rewrite the above equation in standard form. d y d x + ( 2 x ) y = 3 x (1) Compare the above equation with standard equation. P ( x ) = 2 x and f ( x ) = 3 x Calculate the integrating factor for the equation. e ∫ P ( x ) d x = e ∫ ( 2 x ) d x = e 2 ln x = e ln x 2 = x 2 Multiply equation (1) with integrating factor

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

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Chapter 2.3, Problem 10E

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The general solution of differential equation, largest interval over which solution is defined and transient term in the general solution of differential equation.

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Chapter 2.3, Problem 9E

Chapter 2.3, Problem 11E

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Chapter 2 Solutions

EBK ADVANCED ENGINEERING MATHEMATICS

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The general solution of differential equation, largest interval over which solution is defined and transient term in the general solution of differential equation.

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Chapter 2 Solutions