Explanation Given: y ′ − y = e x Concept used: The general solution of the first order linear differential equation of the form y ′ + P y = Q , where P and Q are constants or functions of x only is, y ⋅ ( IF ) = ∫ Q ⋅ ( IF ) d x + c where IF = integrating factor = e ∫ P d x and c is any arbitrary constant . Calculation: Comparing the given linear differential equation y ′ − y = e x with y ′ + P y = Q , we get P = − 1 and Q = e x . ∴ Integrating factor = e ∫ P d x Ȁ

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ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 9.5, Problem 14E

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To find the general solution of the linear differential equation y′−y=ex.

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EBK CALCULUS: EARLY TRANSCENDENTALS

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To find the general solution of the linear differential equation y ′ − y = e x .

Solution Summary: The author explains the general solution of the linear differential equation yprime.

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To find the general solution of the linear differential equation y′−y=ex.

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Chapter 9 Solutions