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Consider the system dx dt = 3x - x² - xy, 1 Critical point 1: (?, ?) Critical point 2: (?, ?) dy a) Find all the critical points (equilibrium solutions). Number of critical points: 4▼ Critical point 3: (?, ?) dt = 2y - 2y² - 3xy Critical point 4: (?, ?) 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.

Consider the system dx dt = 3x - x² - xy, 1 Critical point 1: (?, ?) Critical point 2: (?, ?) dy a) Find all the critical points (equilibrium solutions). Number of critical points: 4▼ Critical point 3: (?, ?) dt = 2y - 2y² - 3xy Critical point 4: (?, ?) 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.

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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Consider the system dx dt - 3x − x² - xy, Critical point 1: (?, ?) a) Find all the critical points (equilibrium solutions). Number of critical points: Critical point 2: (?, ?) dy dt Critical point 3: (?, ?) = 2y - 2y² - 3xy Critical point 4: (?, ?) 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.
Transcribed Image Text:Consider the system dx dt - 3x − x² - xy, Critical point 1: (?, ?) a) Find all the critical points (equilibrium solutions). Number of critical points: Critical point 2: (?, ?) dy dt Critical point 3: (?, ?) = 2y - 2y² - 3xy Critical point 4: (?, ?) 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.
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. Critical point 1 is a Choose one and is Choose one ▾ Critical point 2 is a Choose one ▾ and is Choose one Critical point 3 is a Choose one ▾ and is Choose one ▾ Critical point 4 is a Choose one and is Choose one
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. Critical point 1 is a Choose one and is Choose one ▾ Critical point 2 is a Choose one ▾ and is Choose one Critical point 3 is a Choose one ▾ and is Choose one ▾ Critical point 4 is a Choose one and is Choose one
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