3.3.6 Exercises Phase Plane Analysis of Linear Systems with Distinct Real Eigenvalues. For each of the linear systems dx/dt = Ax in Exercise Group 3.3.6.1-4 a. Find the eigenvalues of A. b. What is the dominant eigenvalue? c. Find the eigenvectors for each eigenvalue of A. d. What are the straight-line solutions of dx/dt = Ax? e. Describe the nature of the equilibrium solution at 0. f. Sketch the phase plane and several solution curves. 1. 3. -1 2 4- (-²3) A= -6 6 = (18⁰ 10 A = -9 -2 0 2. 4. = (-12 30) -5 6. Consider the linear system dx/dt = Ax, where 4-(32₂)- A= = A 8 4-(-112$) A = 5. Solve each linear systems dx/dt = Ax in Exercise Group 3.3.6.1-4 for the initial condition x(0) = (2, 2).
3.3.6 Exercises Phase Plane Analysis of Linear Systems with Distinct Real Eigenvalues. For each of the linear systems dx/dt = Ax in Exercise Group 3.3.6.1-4 a. Find the eigenvalues of A. b. What is the dominant eigenvalue? c. Find the eigenvectors for each eigenvalue of A. d. What are the straight-line solutions of dx/dt = Ax? e. Describe the nature of the equilibrium solution at 0. f. Sketch the phase plane and several solution curves. 1. 3. -1 2 4- (-²3) A= -6 6 = (18⁰ 10 A = -9 -2 0 2. 4. = (-12 30) -5 6. Consider the linear system dx/dt = Ax, where 4-(32₂)- A= = A 8 4-(-112$) A = 5. Solve each linear systems dx/dt = Ax in Exercise Group 3.3.6.1-4 for the initial condition x(0) = (2, 2).
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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3.3.6 Exercises
Phase Plane Analysis of Linear Systems with Distinct Real Eigenvalues.
For each of the linear systems dx/dt = Ax in Exercise Group 3.3.6.1-4
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a. Find the eigenvalues of A.
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e. Describe the nature of the equilibrium solution at 0.
f. Sketch the phase plane and several solution curves.
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