(i) Solve the initial-value problem x' Ax with x(0) = (3, 2). (ii) Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system. (iii) Find the directions of greatest attraction and/or repulsion. (iv) When the origin is a saddle point, sketch typical trajectories. -2 (a) A = 1 [7 -5 (b) A = 4 Answer: (a) The origin is a saddle point. The direction of G.A. = -5 The direction of G.R. %3D Answer: (b) The origin is a repeller. The direction of G.R. =

(i) Solve the initial-value problem x' Ax with x(0) = (3, 2). (ii) Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system. (iii) Find the directions of greatest attraction and/or repulsion. (iv) When the origin is a saddle point, sketch typical trajectories. -2 (a) A = 1 [7 -5 (b) A = 4 Answer: (a) The origin is a saddle point. The direction of G.A. = -5 The direction of G.R. %3D Answer: (b) The origin is a repeller. The direction of G.R. =

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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