Program Explanation Given information: The differential linear systemand the initial conditions are, x ′ = [ − 3 2 − 3 4 ] x , x 1 ( 0 ) = 0 and x 2 ( 0 ) = 5 Explanation: The given differential linear system and the initial conditions are, x ′ = [ − 3 2 − 3 4 ] , x 1 ( 0 ) = 0 and x 2 ( 0 ) = 5 To verify that the vector functions x 1 and x 2 are solutions of matrix differential function, the vector functions x 1 and x 2 are calculated as, x 1 = [ e 3 t 3 e 3 t ] ⇒ x 1 ′ = [ 3 e 3 t 9 e 3 t ] x 2 = [ 2 e − 2 t e − 2 t ] ⇒ x 2 ′ = [ − 4 e − 2 t − 2 e − 2 t ] The coefficient matrix P is calculated as, P x 1 = [ − 3 2 − 3 4 ] [ e 3 t 3 e 3 t ] P x 1 = [ 3 e 3 t 9 e 3 t ] = x 1 ′ P x 2 = [ − 3 2 − 3 4 ] [ 2 e − 2 t e − 2 t ] P x 2 = [ − 4 e − 2 t − 2 e − 2 t ] = x 2 ′ The Wronskian of solution is calculated as, W = | e 3 t e 3 t 2 e − 2 t e − 2 t | = e t − 2 e t = − e t Since the Wronskian of solution is never zero. Therefore, x 1 and x 2 are linearly independent

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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Chapter 5.1, Problem 31P

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Program Description: Purpose of problem is to find the particular solution of the differential linear system with initial conditions.

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Chapter 5.1, Problem 30P

Chapter 5.1, Problem 32P

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In Problems 1-24, find the general solution of the given differ- ential equation. Give the largest interval over which the general solution is defined. Determine whether there are any transient terms in the general solution. 8. y' 2y + x² + 5

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 problem is to find the particular solution of the differential linear system with initial conditions.

Solution Summary: The author explains that the problem is to find the particular solution of the differential linear system with initial conditions.

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Program Description: Purpose of problem is to find the particular solution of the differential linear system with initial conditions.

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Chapter 5 Solutions