i. Find all critical points (equilibria). ii. Determine the linearized system for each of the points in (i.). Classify each of the critical points (equilibria). If the critical points are not spirals or centers, find all eigenvectors. iii. Sketch the global phase portrait. Include the eigenvectors for the linearized system at each critical point and draw arrowws on the solution curves to indicate the direction of flow. a) x' = x² – x + y, y' = 2x² – 2x %3D

i. Find all critical points (equilibria). ii. Determine the linearized system for each of the points in (i.). Classify each of the critical points (equilibria). If the critical points are not spirals or centers, find all eigenvectors. iii. Sketch the global phase portrait. Include the eigenvectors for the linearized system at each critical point and draw arrowws on the solution curves to indicate the direction of flow. a) x' = x² – x + y, y' = 2x² – 2x %3D

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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