Explanation Formula used: Integrating factor: The integrating factor of the First-order linear Differential equation y ′ + f ( x ) y = g ( x ) is I ( x ) = e ∫ f ( x ) d x . Calculation: The given equation is y ′ − 2 y = 4 x . From the differential equation y ′ − 2 y = 4 x , it is observed that f ( x ) = − 2 and g ( x ) = 4 x . I ( x ) = e ∫ − 2 d x = e − 2 x Thus, the integrating factor of the differential equation y ′ − 2 y = 4 x is e − 2 x . Multiply both sides of the equation y ′ − 2 y = 4 x by the integrating factor e − 2 x . e − 2 x y ′ − 2 e − 2 x y = 4 x e − 2 x ( e − 2 x y ) ′ = 4 x e − 2 x [ ∵ ( x y ) ′ = x y ′ + x ′ y ] Integrate both sides of the above equation

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Differential Equations

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Chapter 9.3, Problem 37E

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To find: The integrating factor and the general solution of the differential equation y′−2y=4x.

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Chapter 9.3, Problem 36E

Chapter 9.3, Problem 38E

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Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

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The integrating factor and the general solution of the differential equation y ′ − 2 y = 4 x .

Solution Summary: The author calculates the integrating factor of the First-order linear Differential equation yprime.

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To find: The integrating factor and the general solution of the differential equation y′−2y=4x.

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Chapter 9 Solutions