Consider the system dy dx 2x - x2- xy, dt = 2y – 2y? - 3ry dt %3D a) Find all the critical points (equilibrium solutions). Number of critical points: 4v Critical point 1: (?, ?) Critical point 2: (?,?) Critical point 3: (?,?) Critical point 4: (?,?) b) Use an appropriate graphing device to draw a direction field and phase portrait for the system.
Consider the system dy dx 2x - x2- xy, dt = 2y – 2y? - 3ry dt %3D a) Find all the critical points (equilibrium solutions). Number of critical points: 4v Critical point 1: (?, ?) Critical point 2: (?,?) Critical point 3: (?,?) Critical point 4: (?,?) b) Use an appropriate graphing device to draw a direction field and phase portrait for the system.
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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![c) From the plot(s) in part b, determine whether each critical point
is asymptotically stable, stable, or unstable, and classify it as to
type.
Critical point 1 is a saddle point X
and is asymptotically stable v
The basin of attraction of the point is in the (open) quadrant (s):
first V second V third fourth
Critical point 2 is a saddle point
and is asymptotically stable
The basin of attraction of the point is in the (open) quadrant (s):
V first second
fourth
Critical point 3 is a saddle point X
and is asymptotically stable -
The basin of attraction of the point is in the (open) quadrant (s):
V first second third
fourth
Critical point 4 is a saddle point v
and is asymptotically stable v
The basin of attraction of the point is in the (open) quadrant (s):
first ]second
third
fourth](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6eea892d-6422-48d4-a666-49531a43da6e%2F1e18d921-df20-41fe-8eb5-e6ab04d02292%2Fnccdd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c) From the plot(s) in part b, determine whether each critical point
is asymptotically stable, stable, or unstable, and classify it as to
type.
Critical point 1 is a saddle point X
and is asymptotically stable v
The basin of attraction of the point is in the (open) quadrant (s):
first V second V third fourth
Critical point 2 is a saddle point
and is asymptotically stable
The basin of attraction of the point is in the (open) quadrant (s):
V first second
fourth
Critical point 3 is a saddle point X
and is asymptotically stable -
The basin of attraction of the point is in the (open) quadrant (s):
V first second third
fourth
Critical point 4 is a saddle point v
and is asymptotically stable v
The basin of attraction of the point is in the (open) quadrant (s):
first ]second
third
fourth
Transcribed Image Text:Consider the system
dx
= 2x – x - xy,
dt
dy
2y – 2y2 - 3xy
dt
a) Find all the critical points (equilibrium solutions).
Number of critical points: 4
Critical point 1: (?, ?)
Critical point 2: (?, ?)
X1
Critical point 3: (?, ?)
Critical point 4: (?,?)
b) Use an appropriate graphing device to draw a direction field and
phase portrait for the system.
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