Program Explanation Given information: The value of Ais [ 6 − 7 1 − 2 ] , f ( t ) = [ 100 t − 50 t ] and e A t = 1 6 [ − e − t + 7 e 5 t 7 e − t − 7 e 5 t − e − t + e 5 t 7 e − t − e 5 t ] . Explanation: The initial value problem can be solving by the variation of parameters method as shown below. x ( t ) = e A t x 0 + 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 | = 1 6 | − e − t + 7 e 5 t 7 e − t − 7 e 5 t − e − t + e 5 t 7 e − t − e 5 t | = 1 6 | ( − e − t + 7 e 5 t ) ( 7 e − t − e 5 t ) − ( 7 e − t − 7 e 5 t ) ( − e − t + e 5 t ) | = e 4 t The determinant of e A t is not 0. The inverse of the matrix is shown below. e − A t = 1 6 | e − A t | adj ( e − A t ) = 1 6 e 4 t [ 7 e − t − e 5 t − 7 e − t + 7 e 5 t e − t − e 5 t − e − t + 7 e 5 t ] = 1 6 [ 7 e − 5 t − e t − 7 e − 5 t + 7 e t e − 5 t − e t − e − 5 t + 7 e 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 1 6 [ 7 e − 5 s − e s − 7 e − 5 s + 7 e s e − 5 s − e s − e − 5 s + 7 e s ] [ 100 s − 50 s ] d s = 1 6 ∫ 0 t [ 1050 s e − 5 s − 450

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optima…

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Chapter 5.7, Problem 18P

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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 17P

Chapter 5.7, Problem 19P

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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