netimes a constant equilibrium solution has the property that solutions lying on one side of the equilibrium solution tend to proach it, whereas solutions lying on the other side depart from it. In this case the equilibrium solution is said to be semistable. ssify the critical (equilibrium) points as asymptotically stable, unstable, or semistable. dy = y° (2 – y²), -∞ < yo < ∞ dt O (- v2,0) is semistable, (0, 0) is unstable, (V2,0), is asymptotically stable. O (- V2,0) is unstable, (0, 0) is asymptotically stable, (y2,0), is semistable. O (- v2,0) is unstable, (0, 0) is semistable, (V2,0), is asymptotically stable. O (- V2,0) is asymptotically stable, (0, 0) is semistable, (y2,0), is unstable. O (- 2 0)is semistable (0.0)is asvmntotically stahle (1/2.0) is unstable
netimes a constant equilibrium solution has the property that solutions lying on one side of the equilibrium solution tend to proach it, whereas solutions lying on the other side depart from it. In this case the equilibrium solution is said to be semistable. ssify the critical (equilibrium) points as asymptotically stable, unstable, or semistable. dy = y° (2 – y²), -∞ < yo < ∞ dt O (- v2,0) is semistable, (0, 0) is unstable, (V2,0), is asymptotically stable. O (- V2,0) is unstable, (0, 0) is asymptotically stable, (y2,0), is semistable. O (- v2,0) is unstable, (0, 0) is semistable, (V2,0), is asymptotically stable. O (- V2,0) is asymptotically stable, (0, 0) is semistable, (y2,0), is unstable. O (- 2 0)is semistable (0.0)is asvmntotically stahle (1/2.0) is unstable
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Sometimes a constant equilibrium solution has the property that solutions lying on one side of the equilibrium solution tend to
approach it, whereas solutions lying on the other side depart from it. In this case the equilibrium solution is said to be semistable.
Classify the critical (equilibrium) points as asymptotically stable, unstable, or semistable.
dy
= y (2 – y²), -* < yo < ∞
dt
O (- v2,0) is semistable, (0, 0) is unstable, (V2,0), is asymptotically stable.
O (- V2,0) is unstable, (0, 0) is asymptotically stable, (y2,0), is semistable.
O (- v2,0) is unstable, (0, 0) is semistable, (V2,0), is asymptotically stable.
O (- v2,0) is asymptotically stable, (0, 0) is semistable, (V2,0), is unstable.
O (- v2,0) is semistable, (0, 0) is asymptotically stable, (V2,0), is unstable.
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