Program Explanation Given information: The differential equation is e y + y cos x + ( x e y + sin x ) y ′ = 0 . Explanation: The given differential equation can be written as, e y + y cos x + ( x e y + sin x ) d y d x = 0 ( e y + y cos x ) d x + ( x e y + sin x ) d y = 0 The general form of exact differential equation is, M ( x , y ) d x + N ( x , y ) d y = 0 The above differential equation is exact if and only if the below condition satisfies, ∂ M d y = ∂ N ∂ x ....... (1) Compare the given differential equation with the general differential equation to obtain the value of M ( x , y ) and N ( x , y ) as, M ( x , y ) = e y + y cos x N ( x , y ) = x e y + sin x Substitute e y + y cos x for M and x e y + sin x for N in equation (1) as, ∂ ∂ y ( e y + y cos x ) = ? ∂ ∂ x ( x e y + sin x ) e y + cos x = e y + cos x Thus, the given differential equation is exact. The value of M ( x , y ) can be written as, M ( x , y ) = ∂ F ∂ x The value of F ( x , y ) can be obtained if both the sides of above equation are integrated with respect to x as, ∫ M ( x , y ) d x = F ( x , y ) <

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 1, Problem 23RP

Program Plan Intro

Program Description: Purpose of problem is to calculate the general solution of the differential equation ey+ycosx+(xey+sinx)y′=0 .

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Chapter 1, Problem 22RP

Chapter 1, Problem 24RP

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose of problem is to calculate the general solution of the differential equation e y + y cos x + ( x e y + sin x ) y ′ = 0 .

Solution Summary: The author explains the purpose of the problem, which is to calculate the general solution to the differential equation.

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Program Description: Purpose of problem is to calculate the general solution of the differential equation ey+ycosx+(xey+sinx)y′=0 .

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Chapter 1 Solutions