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Consider the following system of linear differential equations: dx dt dy dt (a) Find the eigenvalues and eigenvectors associated with the system. (b) Draw the x and y-nullclines in the phase plane. In each region of the complement of the nullclines and on each nullcline, draw at least one direction arrow. (c) Find the equilibrium and classify it. (d) Find the particular solution for the initial value x(0) = 4, y(0) = -15. (e) Sketch the solution curve for the initial value x(0) = −1, y(0) = 2 in the phase plane. Question 16. -6x - 2y 22x +9y

Consider the following system of linear differential equations: dx dt dy dt (a) Find the eigenvalues and eigenvectors associated with the system. (b) Draw the x and y-nullclines in the phase plane. In each region of the complement of the nullclines and on each nullcline, draw at least one direction arrow. (c) Find the equilibrium and classify it. (d) Find the particular solution for the initial value x(0) = 4, y(0) = -15. (e) Sketch the solution curve for the initial value x(0) = −1, y(0) = 2 in the phase plane. Question 16. -6x - 2y 22x +9y

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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Question 16. Consider the following system of linear differential equations: dx dt - = -6x - 2y 22x +9y dt (a) Find the eigenvalues and eigenvectors associated with the system. (b) Draw the x and y-nullclines in the phase plane. In each region of the complement of the nullclines and on each nullcline, draw at least one direction arrow. (c) Find the equilibrium and classify it. (d) Find the particular solution for the initial value x(0) = 4, y(0) = = -15. (e) Sketch the solution curve for the initial value x(0) = −1, y(0) = 2 in the phase plane.
Transcribed Image Text:Question 16. Consider the following system of linear differential equations: dx dt - = -6x - 2y 22x +9y dt (a) Find the eigenvalues and eigenvectors associated with the system. (b) Draw the x and y-nullclines in the phase plane. In each region of the complement of the nullclines and on each nullcline, draw at least one direction arrow. (c) Find the equilibrium and classify it. (d) Find the particular solution for the initial value x(0) = 4, y(0) = = -15. (e) Sketch the solution curve for the initial value x(0) = −1, y(0) = 2 in the phase plane.
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