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Consider the system T1 = T2 = The eigenvectors are dx dt where x is a 2 x 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. 1 (³² 3-20 -5 X 2)-(5 and P) 1 b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a [Choose one and is Choose one c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of a versus t and x2 versus t.

Consider the system T1 = T2 = The eigenvectors are dx dt where x is a 2 x 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. 1 (³² 3-20 -5 X 2)-(5 and P) 1 b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a [Choose one and is Choose one c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of a versus t and x2 versus t.

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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Consider the system 71 = 72 = The eigenvectors are dx dt 1 = where x is a 2 x 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. 3 - 20 -5 X )-(5 and 1 b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a [Choose one and is Choose one c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of ₁ versus t and x2 versus t.
Transcribed Image Text:Consider the system 71 = 72 = The eigenvectors are dx dt 1 = where x is a 2 x 1 vector. a) Find the eigenvalues r₁, 72 and the corresponding eigenvectors. 3 - 20 -5 X )-(5 and 1 b) Classify the critical point (0,0) as to type, and determine whether it is stable, asymptotically stable, or unstable. The origin is a [Choose one and is Choose one c) Sketch, by hand (without using any graphing device), several trajectories in the phase plane. d) Use an appropriate graphing device to plot accurately several trajectories in the phase plane and the corresponding graphs of ₁ versus t and x2 versus t.
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