Explanation Given: The solution of first-order differential equation y ′ = y − y 2 is y = 1 1 + c 1 e − x and initial condition is y ( 0 ) = − 1 3 . Calculation: Consider the differential equation, d y d x = cos ( x + y ) (1) Consider the equation, u = x + y Differentiate the equation with respect to x . d u d x = 1 + d y d x d u d x − 1 = d y d x (2) Substitute the value of d y d x and x + y in equation (1), d u d x − 1 = cos u d u d x = 1 + cos u d u 1 + cos u = d x (3) Integrate the equation (3)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.5, Problem 29E

To determine

The solution of the given differential equation.

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Chapter 2.5, Problem 28E

Chapter 2.5, Problem 30E

Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E 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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Chapter 2 Solutions