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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
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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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.)

 
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.
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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