Explanation Given: The differential equation is x 2 d y d x − y = x 3 with the initial condition y ( 1 ) = 0 . Procedure used: The standard form of the first order linear differential equation with initial condition y ( x 0 ) = y 0 is, d y d x + P ( x ) y = Q ( x ) (1) To solve the equation (1) for y ( x ) , use the integrating factor method. The integrating factor of the differential equation is e ∫ P ( x ) d x . And the solution of the differential equation is, y ⋅ ( Integrating factor ) = ∫ ( ( Integrating factor ) ⋅ ( Q ( x ) ) ) d x + C (2) Here, C is constant. Calculation: The differential equation with initial condition y ( 1 ) = 0 is, x 2 d y d x − y = x 3 d y d x − y x 2 = x 3 x 2 d y d x − y x 2 = x (3) Compare equation (3) with equation (1). P ( x ) = − 1 x 2 and Q ( x ) = x Therefore the integrating factor of the differential equation (3) is, I . F = e ∫ − 1 x 2 d x = e 1 x Substitute e 1 x for integrating factor and x for Q ( x ) in equation (2)

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Differential Equations

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Chapter 2.3, Problem 46E

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The solution in the terms of an integral-defined function.

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Chapter 2.3, Problem 45E

Chapter 2.3, Problem 47E

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Chapter 2 Solutions

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...

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The solution in the terms of an integral-defined function.

Solution Summary: The author explains the solution of the initial value problem in the terms of an integral-defined function.

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Chapter 2 Solutions