Explanation Given: The differential equation is y d x = ( y e x − 2 x ) d y . Procedure used: Linear equation in standard form: d x d y + P ( y ) x = Q ( y ) The integrating factor of the linear equation: I F = e ∫ P ( y ) d y Solution of linear differential equation: x ⋅ I F = ∫ Q ( y ) ⋅ I F d y Calculation: Consider the given differential equation, y d x = ( y e x − 2 x ) d y Arrange the given differential equation in suitable form. y d x = ( y e x − 2 x ) d y d x d y = y e y − 2 x y d x d y = e y − 2 y x Compare the equation with the standard form d x d y + P ( y ) x = Q ( y ) . P ( y ) = 2 y and Q ( y ) = e y . Write the expression for integrating factor. I F = e ∫ P ( y ) d y (1) Substitute 2 y for P ( y ) in the equation (1). I F = e ∫ ( 2 y ) d y = e 2 ln y = e ln y 2 = y 2 Write the expression for solution of y

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 16E

To determine

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

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Chapter 2.3, Problem 15E

Chapter 2.3, Problem 17E

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Chapter 2 Solutions

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