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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 y²(5 – y² ). – * < yo < * dt O (- V5,0) is unstable, (0, 0) is asymptotically stable, (V5,0), is semistable. O (- V5,0) is unstable, (0, 0) is semistable, (V5,0), is asymptotically stable. O (- V5,0) is semistable, (0, 0) is unstable, (V5,0), is asymptotically stable. O (- V5,0) is asymptotically stable, (0, 0) is semistable, (5,0), is unstable. O (- V5,0) is semistable, (0, 0) is asymptotically stable, (V5,0), is unstable. eTextbook and Media Save for Later Attempts: 0 of 3 used Submit Answer

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 y²(5 – y² ). – * < yo < * dt O (- V5,0) is unstable, (0, 0) is asymptotically stable, (V5,0), is semistable. O (- V5,0) is unstable, (0, 0) is semistable, (V5,0), is asymptotically stable. O (- V5,0) is semistable, (0, 0) is unstable, (V5,0), is asymptotically stable. O (- V5,0) is asymptotically stable, (0, 0) is semistable, (5,0), is unstable. O (- V5,0) is semistable, (0, 0) is asymptotically stable, (V5,0), is unstable. eTextbook and Media Save for Later Attempts: 0 of 3 used Submit Answer

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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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 y²(5 – y² ). – * < yo < * dt O (- V5,0) is unstable, (0, 0) is asymptotically stable, (V5,0), is semistable. O (- V5,0) is unstable, (0, 0) is semistable, (V5,0), is asymptotically stable. O (- V5,0) is semistable, (0, 0) is unstable, (V5,0), is asymptotically stable. O (- V5,0) is asymptotically stable, (0, 0) is semistable, (5,0), is unstable. O (- V5,0) is semistable, (0, 0) is asymptotically stable, (V5,0), is unstable. eTextbook and Media Save for Later Attempts: 0 of 3 used Submit Answer
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 y²(5 – y² ). – * < yo < * dt O (- V5,0) is unstable, (0, 0) is asymptotically stable, (V5,0), is semistable. O (- V5,0) is unstable, (0, 0) is semistable, (V5,0), is asymptotically stable. O (- V5,0) is semistable, (0, 0) is unstable, (V5,0), is asymptotically stable. O (- V5,0) is asymptotically stable, (0, 0) is semistable, (5,0), is unstable. O (- V5,0) is semistable, (0, 0) is asymptotically stable, (V5,0), is unstable. eTextbook and Media Save for Later Attempts: 0 of 3 used Submit Answer
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