(a) Explanation Given: d y d x = y , y ( 0 ) = 1 And, d y d x = y + y x ln x , y ( e ) = 1 Calculation: Consider the given equation. d y d x = y Separate the variables of the above equation. d y y = d x Integrate the above equation. ∫ d y y = ∫ d x ln | y | = x + c Substitute 1 for y and 0 for x in above equation. ln | 1 | = 0 + c c = 0 Hence the solution is, ln | y | = x y = e x [ Exponentiating both sides ] Consider the given equation. d y d x = y + y x ln x Separate the variables of the above equation. d y d x = y ( 1 + 1 x ln x ) d y y = ( 1 + 1 x ln x ) d x Integrate the above equation (b) To determine To show: There are more than 1.65 million digits in the y -coordinate of the point of intersection of the two solution curves.

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Differential Equations

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Chapter 2.2, Problem 54E

(a)

To determine

The solution of the given initial value problem.

(b)

To determine

To show: There are more than 1.65 million digits in the y-coordinate of the point of intersection of the two solution curves.

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Chapter 2.2, Problem 53E

Chapter 2.2, Problem 55E

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Chapter 2 Solutions

Differential Equations with Boundary-Value Problems (MindTap Course List)

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 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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The solution of the given initial value problem.

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The solution of the given initial value problem.

To show: There are more than 1.65 million digits in the y-coordinate of the point of intersection of the two solution curves.

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Chapter 2 Solutions