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x(t) = f(x,y) dt y(t) = f(x,y), that has precisely two equilibrium points, both of which are saddle points, denote by (x,y) and (x,y). Sketch the phase portrait where there is a trajectory th connects (x,y) with (x,y). How does this trajectory relate to the eigenvalues ar eigenvectors of the Jacobian matrix evaluated at each of the equilibrium points?

x(t) = f(x,y) dt y(t) = f(x,y), that has precisely two equilibrium points, both of which are saddle points, denote by (x,y) and (x,y). Sketch the phase portrait where there is a trajectory th connects (x,y) with (x,y). How does this trajectory relate to the eigenvalues ar eigenvectors of the Jacobian matrix evaluated at each of the equilibrium points?

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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H5. Consider an ODE x(t) = f(x,y) dt d y(t) = f(x,y), that has precisely two equilibrium points, both of which are saddle points, denoted by (x,y) and (x,y). Sketch the phase portrait where there is a trajectory that connects (x,y) with (x2,y2). How does this trajectory relate to the eigenvalues and eigenvectors of the Jacobian matrix evaluated at each of the equilibrium points? Hint: Write down your thought process, even if you don't manage to solve this problem.
Transcribed Image Text:H5. Consider an ODE x(t) = f(x,y) dt d y(t) = f(x,y), that has precisely two equilibrium points, both of which are saddle points, denoted by (x,y) and (x,y). Sketch the phase portrait where there is a trajectory that connects (x,y) with (x2,y2). How does this trajectory relate to the eigenvalues and eigenvectors of the Jacobian matrix evaluated at each of the equilibrium points? Hint: Write down your thought process, even if you don't manage to solve this problem.
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