Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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El. Consider the autonomous ODE below in which a is a constant (real mumber):
/ =a+cos(y)
a) For what value(s) of a, if any, would there be no critical points (equilibrium/constant solu-
táons)?
b) For what value(s) of a, if any, would all critical points (equilibrium/constant solutions) be
semi-stable?
e) Suppose a =
Determine a value of yo for which the solution would be increasing.
0 and consider the specific solution savisfying the initial condition v(0) = %0-
%3D
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Transcribed Image Text:El. Consider the autonomous ODE below in which a is a constant (real mumber): / =a+cos(y) a) For what value(s) of a, if any, would there be no critical points (equilibrium/constant solu- táons)? b) For what value(s) of a, if any, would all critical points (equilibrium/constant solutions) be semi-stable? e) Suppose a = Determine a value of yo for which the solution would be increasing. 0 and consider the specific solution savisfying the initial condition v(0) = %0- %3D
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