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For the system: dx = y(2 + x − x²) and dt a. Find all the critical points. dy = dt (2+x)(y-x) b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable. c. Describe the basin of attraction for each asymptotically stable critical point.

For the system: dx = y(2 + x − x²) and dt a. Find all the critical points. dy = dt (2+x)(y-x) b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable. c. Describe the basin of attraction for each asymptotically stable critical point.

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For the system: dx = y(2 + x − x²) and dt a. Find all the critical points. dy = dt (2+x)(y-x) b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable. c. Describe the basin of attraction for each asymptotically stable critical point.
Transcribed Image Text:For the system: dx = y(2 + x − x²) and dt a. Find all the critical points. dy = dt (2+x)(y-x) b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable. c. Describe the basin of attraction for each asymptotically stable critical point.
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