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Consider the system dx dy = (4- x)(y-x), = y(4-3x - x²) dt dt a) Find all the critical points (equilibrium solutions). ✓ Number of critical points: Critical point 1: (0,0) Critical point 2: (4,4) Critical point 3: (-1,-1) X X Critical point 4: (4,0) b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point

Consider the system dx dy = (4- x)(y-x), = y(4-3x - x²) dt dt a) Find all the critical points (equilibrium solutions). ✓ Number of critical points: Critical point 1: (0,0) Critical point 2: (4,4) Critical point 3: (-1,-1) X X Critical point 4: (4,0) b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point

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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b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point. Critical point 1 is a center: and is stable Critical point 2 is a saddle point and is unstable Critical point 3 is a nodal point and is unstable Critical point 4 is a spiral point and is unstable X X X X X X X
Transcribed Image Text:b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point. Critical point 1 is a center: and is stable Critical point 2 is a saddle point and is unstable Critical point 3 is a nodal point and is unstable Critical point 4 is a spiral point and is unstable X X X X X X X
Your answer is partially correct. Consider the system 1055 dx dy dt = (4- x)(y-x), dt a) Find all the critical points (equilibrium solutions). Number of critical points: 4 Critical point 1: (0,0) Critical point 2: (4,4) Critical point 3: (-1,-1) Critical point 4: (4,0) X = y(4-3x - x²) X ✓ b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point
Transcribed Image Text:Your answer is partially correct. Consider the system 1055 dx dy dt = (4- x)(y-x), dt a) Find all the critical points (equilibrium solutions). Number of critical points: 4 Critical point 1: (0,0) Critical point 2: (4,4) Critical point 3: (-1,-1) Critical point 4: (4,0) X = y(4-3x - x²) X ✓ b) Use an appropriate graphing device to draw a direction field and phase portrait for the system. 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. Describe the basin of attraction for each asymptotically stable critical point
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