Program Explanation Given information: The value of Ais [ 2 − 5 1 − 2 ] , f ( t ) = [ 4 cos t 6 sin t ] , x ( 0 ) = [ 3 5 ] and e A t = [ cos t + 2 sin t − 5 sin t sin t cos t − 2 sin t ] . Explanation: The initial value problem can be solving by the variation of parameters method as shown below. x ( t ) = e A t x 1 + e A t ∫ 0 t e − A s f ( s ) d s The determinant of e A t can be obtain as, | e A t | = [ cos t + 2 sin t − 5 sin t sin t cos t − 2 sin t ] = | cos 2 t − 4 sin 2 t + 5 sin 2 t | = sin 2 t + cos 2 t = 1 The determinant of e A t is not 0. Therefore the inverse of the matrix is shown below. e − A t = 1 | e − A t | adj ( e − A t ) = adj [ cos t + 2 sin t − 5 sin t sin t cos t − 2 sin t ] = [ cos t − 2 sin t 5 sin t − sin t cos t + 2 sin t ] The value of ∫ 0 t e − A s f ( s ) d s can be obtained as, ∫ 0 t e − A s f ( s ) d s = ∫ 0 t [ cos s − 2 sin s 5 sin

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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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 5.7, Problem 26P

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Program Description:Purpose of problem is to solve the initial value problem x′=Ax+f(t) and x(a)=xa by using method of variation of parameters.

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Chapter 5.7, Problem 25P

Chapter 5.7, Problem 27P

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Chapter 5 Solutions

EBK DIFFERENTIAL EQUATIONS

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 problem is to solve the initial value problem x ′ = A x + f ( t ) and x ( a ) = x a by using method of variation of parameters.

Solution Summary: The author explains that the initial value problem can be solved by the variation of parameters method as shown below.

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Program Description:Purpose of problem is to solve the initial value problem x′=Ax+f(t) and x(a)=xa by using method of variation of parameters.

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Chapter 5 Solutions