Explanation Procedure used: Consider the first order differential equation: M ( x , y ) d x + N ( x , y ) d y = 0 Find out M x and N y The condition for the exact differential is given by, M y = N x Where, M y is ∂ M ∂ y and N x is ∂ N ∂ x . Calculation: Consider the differential equation in the general form. ( cos x sin x − x y 2 ) d x + y ( 1 − x 2 ) d y = 0 (1) Compare and obtain, M ( x , y ) = ( cos x sin x − x y 2 ) (2) N ( x , y ) = y ( 1 − x 2 ) (3) Partially differentiate the equation (2) with respect to y . M y ( x , y ) = − 2 x y Partially differentiate the equation (3) with respect to x . N x ( x , y ) = − 2 x y Here, M y = N x therefore the equation (1) is exact. Integrate M ( x , y ) with respect to d x considering y as a constant and N ( x , y ) with respect to d y considering x as a constant from equation (1)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 2.4, Problem 41E

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To explain: The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at (−1, 1).

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Chapter 2.4, Problem 40E

Chapter 2.4, Problem 42E

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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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The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at ( − 1 , 1 ) .

Solution Summary: The author explains the definition of the explicit solution of IVP at (-1,1).

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To explain: The definition of the explicit solution of the IVP (the blue curve in Figure 2.4.1) at (−1, 1).

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Chapter 2 Solutions