1. Consider the system x' = 3x + 2y y' = -x (a) Find the general solution of the system. (Ъ) Determine the type of the equilibrium at the origin. (c) Determine the stability of the equilibrium at the origin. (d) • in a saddle/node case, show the eigenvectors and the ray solutions. • in a center/spiral case, determine the direction of rotation. Sketch trajectories in the phase plane. Moreover,

1. Consider the system x' = 3x + 2y y' = -x (a) Find the general solution of the system. (Ъ) Determine the type of the equilibrium at the origin. (c) Determine the stability of the equilibrium at the origin. (d) • in a saddle/node case, show the eigenvectors and the ray solutions. • in a center/spiral case, determine the direction of rotation. Sketch trajectories in the phase plane. Moreover,

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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