Program Explanation Given information: The differential equation is ( 6 x 2 − 8 x 1 ) d x 1 + ( 6 x 1 − 17 x 2 ) d x 2 = 0 . Explanation: The differential equation of the type M d x 1 + N d x 2 = 0 is to be exact if it follows the condition ∂ M ∂ x 2 = ∂ N ∂ x 1 . The given differential equation is ( 6 x 2 − 8 x 1 ) d x 1 + ( 6 x 1 − 17 x 2 ) d x 2 = 0 . Compare the given differential equation with the general equation to obtain the value of M and N . M = ( 6 x 2 − 8 x 1 ) , N = ( 6 x 1 − 17 x 2 ) Now find the partial derivative of M and N to check whether the equation is exact or not. Find the partial derivative of M = ( 6 x 2 − 8 x 1 ) with respect to x 2 as, ∂ M ∂ x 2 = ∂ ∂ x 2 ( 6 x 2 − 8 x 1 ) ∂ M ∂ x 2 = 6 Find the partial derivative of N = ( 6 x 1 − 17 x 2 ) with respect to x 2 as, ∂ N ∂ x 1 = ∂ ∂ x 1 ( 6 x 1 − 17 x 2 ) ∂ N ∂ x 1 = 6 It can be seen that the partial derivatives of M and N are equal as ∂ M ∂ x 2 = ∂ N ∂ x 1 Thus, the given differential equation is exact

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 5.3, Problem 35P

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Program Description: Purpose of the problem is to verify that the equation (6x2−8x1)dx1+(6x1−17x2)dx2=0 with the general solution 4x12+6x1x2−172x22=k .

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Chapter 5.3, Problem 34P

Chapter 5.3, Problem 36P

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Chapter 5 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2P Ch. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

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Program Description: Purpose of the problem is to verify that the equation ( 6 x 2 − 8 x 1 ) d x 1 + ( 6 x 1 − 17 x 2 ) d x 2 = 0 with the general solution 4 x 1 2 + 6 x 1 x 2 − 17 2 x 2 2 = k .

Solution Summary: The author explains the purpose of the problem: to verify that the equation (6x_2) is exact with the general solution.

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Program Description: Purpose of the problem is to verify that the equation (6x2−8x1)dx1+(6x1−17x2)dx2=0 with the general solution 4x12+6x1x2−172x22=k .

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Chapter 5 Solutions