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Consider the system of differential equations For this system, the smaller eigenvalue is da dt dy dt = = -1.4x +0.75y, 1.66667x 3.4y. and the larger eigenvalue is

Consider the system of differential equations For this system, the smaller eigenvalue is da dt dy dt = = -1.4x +0.75y, 1.66667x 3.4y. and the larger eigenvalue is

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Consider the system of differential equations For this system, the smaller eigenvalue is = dx dt dy dt = = = -1.4x +0.75y, 1.66667x3.4y. [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. and the larger eigenvalue is The solution to the above differential equation with initial values ï(0) = 4, y(0) = 3 is x(t): y(t) =
Transcribed Image Text:Consider the system of differential equations For this system, the smaller eigenvalue is = dx dt dy dt = = = -1.4x +0.75y, 1.66667x3.4y. [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves would race towards zero and then veer away towards infinity. (Saddle) The solution curves converge to different points. and the larger eigenvalue is The solution to the above differential equation with initial values ï(0) = 4, y(0) = 3 is x(t): y(t) =
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