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11. Consider the system of differential equations dr = -x-2y dt dy - 2x-y dt a. Show that A = -1±2i are the eigenvalues for this system. b. Sketch the phase portrait. c. Classify the system by stating whether the origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. / d. Find the eigenvectors and write out the general real solution to the system.

11. Consider the system of differential equations dr = -x-2y dt dy - 2x-y dt a. Show that A = -1±2i are the eigenvalues for this system. b. Sketch the phase portrait. c. Classify the system by stating whether the origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. / d. Find the eigenvectors and write out the general real solution to the system.

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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Sketch the phase portr classiry system by Stating origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. 11. Consider the system of differential equations dr =-I-2y dt dy - 2.r - y dt a. Show that A = -1±2i are the eigenvalues for this system. / %3D b. Sketch the phase portrait. c. Classify the system by stating whether the origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. / d. Find the eigenvectors and write out the general real solution to the system. 12. Compute the Laplace transform or inverse Laplace transform using the table and theorems of Laplace transforms. /
Transcribed Image Text:Sketch the phase portr classiry system by Stating origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. 11. Consider the system of differential equations dr =-I-2y dt dy - 2.r - y dt a. Show that A = -1±2i are the eigenvalues for this system. / %3D b. Sketch the phase portrait. c. Classify the system by stating whether the origin is a stable or unstable node, stable or unstable spiral, stable center, or saddle point. / d. Find the eigenvectors and write out the general real solution to the system. 12. Compute the Laplace transform or inverse Laplace transform using the table and theorems of Laplace transforms. /
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