Let X = X(t) be the response of the linear dynamical system x' = ax - By y' = Bx + ay that satisfies the initial condition X(0) = X. Determine conditions on the real constants a and ß that will ensure lim X(t) = (0, 0). (Enter your answer as a comma-separated list of equations and inequalities.) Can (0, 0) be a node or saddle point? O It can be a saddle point but not a node. O It cannot be a node or a saddle point. O It can be a node but not a saddle point. O It can be a node or a saddle point. O There is not enough information to decide.
Let X = X(t) be the response of the linear dynamical system x' = ax - By y' = Bx + ay that satisfies the initial condition X(0) = X. Determine conditions on the real constants a and ß that will ensure lim X(t) = (0, 0). (Enter your answer as a comma-separated list of equations and inequalities.) Can (0, 0) be a node or saddle point? O It can be a saddle point but not a node. O It cannot be a node or a saddle point. O It can be a node but not a saddle point. O It can be a node or a saddle point. O There is not enough information to decide.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Let
X = X(t)
be the response of the linear dynamical system
| x' | = | ?x − ?y |
| y' | = | ?x + ?y |
that satisfies the initial condition
X(0) = X0.
Determine conditions on the real constants ? and ? that will ensure
lim t→∞ X(t) = (0, 0).
(Enter your answer as a comma-separated list of equations and inequalities.)
Transcribed Image Text:Let X = X(t) be the response of the linear dynamical system
x'
= ax
By
y'
Вх + аy
that satisfies the initial condition X(0) = X,:
Determine conditions on the real constants a and ß that will ensure lim X(t) = (0, 0). (Enter your answer as a comma-separated list of equations and inequalities.)
Can (0, 0) be a node or saddle point?
O It can be a saddle point but not a node.
It cannot be a node or a saddle point.
It can be a node but not a saddle point.
It can be a node or a saddle point.
There is not enough information to decide.
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