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Write each system in matrix form- = Ax. dx dt Determine the eigenvalues of A. State whether the origin is a stable or unstable e State whether the origin is a node, saddle point, s State the equations of the straight-line trajectorie owards or away from the origin. If none exist, st A has real eigenvalues, then determine the eige olve the system. (See examples in Section 7.4) x = x + 4y It y It = 4x + y

Write each system in matrix form- = Ax. dx dt Determine the eigenvalues of A. State whether the origin is a stable or unstable e State whether the origin is a node, saddle point, s State the equations of the straight-line trajectorie owards or away from the origin. If none exist, st A has real eigenvalues, then determine the eige olve the system. (See examples in Section 7.4) x = x + 4y It y It = 4x + y

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 D, E, and F. I added the photo that has the first parts completed.

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) 4. dx dt dy dt = x + 4y = 4x + y
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) 4. dx dt dy dt = x + 4y = 4x + y
dy 4a) de = x+4y = 4x+y b) [1-> < unstable 4 [*2] = [41] [4] A= [41] (1-7) ² 2²-2x-15=0 (7-5) (x+3) =0 equilibrium [5 and M
Transcribed Image Text:dy 4a) de = x+4y = 4x+y b) [1-> < unstable 4 [*2] = [41] [4] A= [41] (1-7) ² 2²-2x-15=0 (7-5) (x+3) =0 equilibrium [5 and M
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