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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
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
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
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.
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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