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e following systems, the origin is the equilibrium point. dž Write each system in matrix form = Ax. dt Determine the eigenvalues of A. State whether the origin is a stable or unstable equilib State whether the origin is a node, saddle point, spiral State the equations of the straight-line trajectories an towards or away from the origin. If none exist, state s If A has real eigenvalues, then determine the eigenvec solve the system. (See examples in Section 7.4) dx = 4x - 13y dt dy = 2x - 6y dt

e following systems, the origin is the equilibrium point. dž Write each system in matrix form = Ax. dt Determine the eigenvalues of A. State whether the origin is a stable or unstable equilib State whether the origin is a node, saddle point, spiral State the equations of the straight-line trajectories an towards or away from the origin. If none exist, state s If A has real eigenvalues, then determine the eigenvec solve the system. (See examples in Section 7.4) dx = 4x - 13y dt dy = 2x - 6y dt

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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Parts B, E, F. I attached a photo of the answered parts. 

For the following systems, the origin is the equilibrium point. dx a) Write each system in matrix form = Ax. dt b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 3. dx dt dt = 4x - 13y = 2x - 6y
Transcribed Image Text:For the following systems, the origin is the equilibrium point. dx a) Write each system in matrix form = Ax. dt b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 3. dx dt dt = 4x - 13y = 2x - 6y
dx 3) de a) a 1> dy dt = 4x-13 F) stable 2x-6y A = [ 2 2 4 -120 d (x) -13 [2²] [23] [4] 2] ما
Transcribed Image Text:dx 3) de a) a 1> dy dt = 4x-13 F) stable 2x-6y A = [ 2 2 4 -120 d (x) -13 [2²] [23] [4] 2] ما
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