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22) Solve the following system of ODEs by computing the eigenvalues and eigenvectors of the coefficient matrix A: where dX dt 3 0 A = 0 1/2 = AX+b 0 -3/2 0 -3/2 1/2 subject to the following generic initial condition: Xº = b= 2 What are admissible initial conditions, Xº, if as t→∞, X remains bounded (i.e., X<∞0). Write down the general form of the initial conditions.

22) Solve the following system of ODEs by computing the eigenvalues and eigenvectors of the coefficient matrix A: where dX dt 3 0 A = 0 1/2 = AX+b 0 -3/2 0 -3/2 1/2 subject to the following generic initial condition: Xº = b= 2 What are admissible initial conditions, Xº, if as t→∞, X remains bounded (i.e., X<∞0). Write down the general form of the initial conditions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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22) Solve the following system of ODEs by computing the eigenvalues and eigenvectors of the coefficient matrix A: where 3 A = 0 dX dt = AX+b 0 0 1/2 -3/2 0 -3/2 1/2 subject to the following generic initial condition: Xº = b= 2 What are admissible initial conditions, Xº, if as t→∞, X remains bounded (i.e., X<∞0). Write down the general form of the initial conditions.
Transcribed Image Text:22) Solve the following system of ODEs by computing the eigenvalues and eigenvectors of the coefficient matrix A: where 3 A = 0 dX dt = AX+b 0 0 1/2 -3/2 0 -3/2 1/2 subject to the following generic initial condition: Xº = b= 2 What are admissible initial conditions, Xº, if as t→∞, X remains bounded (i.e., X<∞0). Write down the general form of the initial conditions.
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