(a) Locate all critical points for the nonlinear system 4. x, = x + 4y = f(x,y) y'=2x-y-r"y = g(z, y) (b) Determine the 2 x 2 matrix of the linearization z' Az at each critical point (â, g) for the system (1). By calculating the eigenvalue(s) and associated eigenvector(s) of these matrices de- termine the nature of each critical point, and sketch the corresponding local tra- jectories in a neighborhood of each critical point.

(a) Locate all critical points for the nonlinear system 4. x, = x + 4y = f(x,y) y'=2x-y-r"y = g(z, y) (b) Determine the 2 x 2 matrix of the linearization z' Az at each critical point (â, g) for the system (1). By calculating the eigenvalue(s) and associated eigenvector(s) of these matrices de- termine the nature of each critical point, and sketch the corresponding local tra- jectories in a neighborhood of each critical point.

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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(a) Locate all critical points for the nonlinear system
4.
x, = x + 4y = f(x,y)
y'=2x-y-r"y = g(z, y)
(b) Determine the 2 x 2 matrix
of the linearization z' Az at each critical point (â, g) for the system (1). By
calculating the eigenvalue(s) and associated eigenvector(s) of these matrices de-
termine the nature of each critical point, and sketch the corresponding local tra-
jectories in a neighborhood of each critical point.

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