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(a) Find the eigenvalues and eigenvectors. (b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. (c) Sketch several trajectories in the phase plane, and also sketch some typical graphs of x₁ versus t. (d) Use a computer to plot accurately the curves requested in part (c).

(a) Find the eigenvalues and eigenvectors. (b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. (c) Sketch several trajectories in the phase plane, and also sketch some typical graphs of x₁ versus t. (d) Use a computer to plot accurately the curves requested in part (c).

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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For each of the systems in Problems 1 through 12: (a) Find the eigenvalues and eigenvectors. (b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. (c) Sketch several trajectories in the phase plane, and also sketch some typical graphs of x₁ versus t. (d) Use a computer to plot accurately the curves requested in part (c). 4. #-G =)x dt
Transcribed Image Text:For each of the systems in Problems 1 through 12: (a) Find the eigenvalues and eigenvectors. (b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. (c) Sketch several trajectories in the phase plane, and also sketch some typical graphs of x₁ versus t. (d) Use a computer to plot accurately the curves requested in part (c). 4. #-G =)x dt
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