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
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.
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24638e23-7712-442e-8ea2-f441f488d4c1%2F11806bb3-bae9-4f92-b1b4-ae0a62ce8b61%2F0l1nl6q_processed.png&w=3840&q=75)
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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