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Consider the equation =ay - y² = y(a — y). dy dt - a) Consider the cases a < 0, a = 0, and a > 0. In each case find the critical points, draw the phase line, and determine whether each critical point is asymptotically stable, semistable, or unstable. If a > 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a < 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a = 0, the only critical point y is Choose one

Consider the equation =ay - y² = y(a — y). dy dt - a) Consider the cases a < 0, a = 0, and a > 0. In each case find the critical points, draw the phase line, and determine whether each critical point is asymptotically stable, semistable, or unstable. If a > 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a < 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a = 0, the only critical point y is Choose one

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 equation =ay - y² = y(a — y). dy dt - a) Consider the cases a < 0, a = 0, and a > 0. In each case find the critical points, draw the phase line, and determine whether each critical point is asymptotically stable, semistable, or unstable. If a > 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a < 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a = 0, the only critical point y is Choose one
Transcribed Image Text:Consider the equation =ay - y² = y(a — y). dy dt - a) Consider the cases a < 0, a = 0, and a > 0. In each case find the critical points, draw the phase line, and determine whether each critical point is asymptotically stable, semistable, or unstable. If a > 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a < 0, we have the unstable critical point y = and the asymptotically stable critical point y = If a = 0, the only critical point y is Choose one
b) In each case sketch several solutions of the equation in the ty-plane. a = 1 a=0 a = -1 Choose one Choose one Choose one c) Draw the bifurcation diagram for the equation. stable Choose one unstable
Transcribed Image Text:b) In each case sketch several solutions of the equation in the ty-plane. a = 1 a=0 a = -1 Choose one Choose one Choose one c) Draw the bifurcation diagram for the equation. stable Choose one unstable
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