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Letx* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating dV (x) dx -||x=x* = 0. Next, if x maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?

Letx* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating dV (x) dx -||x=x* = 0. Next, if x maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?

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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Letx* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating dV (x) dx -||x=x* = 0. Next, if x* maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?
Transcribed Image Text:Letx* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating dV (x) dx -||x=x* = 0. Next, if x* maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?
d dt = x(t) = f(x). (2)
Transcribed Image Text:d dt = x(t) = f(x). (2)
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