2.5.1 (Reaching a fixed point in a finite time) A particle travels on the half-line x > 0 with a velocity given by x= -x, where c is real and constant. a) Find all values of c such that the origin x = 0 is a stable fixed point. b) Now assume that c is chosen such that x = 0 is stable. Can the particle ever reach the origin in a finite time? Specifically, how long does it take for the parti- cle to travel from x = 1 to x = 0, as a function of c ?
2.5.1 (Reaching a fixed point in a finite time) A particle travels on the half-line x > 0 with a velocity given by x= -x, where c is real and constant. a) Find all values of c such that the origin x = 0 is a stable fixed point. b) Now assume that c is chosen such that x = 0 is stable. Can the particle ever reach the origin in a finite time? Specifically, how long does it take for the parti- cle to travel from x = 1 to x = 0, as a function of c ?
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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