Consider the scalar differential equation d = x(t) = f(x). dt Define the potential V(x) by Use the chain rule to show that dV (x) dx = -f(x). V(x(t)) ≤ 0. dt
Consider the scalar differential equation d = x(t) = f(x). dt Define the potential V(x) by Use the chain rule to show that dV (x) dx = -f(x). V(x(t)) ≤ 0. dt
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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Transcribed Image Text:Consider the scalar differential equation
d
= x(t) = f(x).
dt
Define the potential V(x) by
Use the chain rule to show that
dV (x)
dx
= -f(x).
V(x(t)) ≤ 0.
dt
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