Consider the system of differential equations For this system, the smaller eigenvalue is -4.1 [Note--you may want to use the WolframAlpha widget (right click to open in a new window). Enter your functions and domain, and then click submit.] If y = Ay is a differential equation, how would the solution curves behave? A. All of the solutions curves would converge towards 0. (Stable node) B. All of the solution curves would run away from 0. (Unstable node) C. The solution curves would race towards zero and then veer away towards infinity. (Saddle) D. The solution curves converge to different points. dx dt The solution to the above differential equation with initial values x(0) = 4, y(0) = 6 is x(t) = 2e^-1.1t+2e^-4.11 y(t) e^-1.1t+50^-4.11 dy dt = -1.6x + 1y. = and the larger eigenvalue is -1.1 1.25x - 3.6y.
Consider the system of differential equations For this system, the smaller eigenvalue is -4.1 [Note--you may want to use the WolframAlpha widget (right click to open in a new window). Enter your functions and domain, and then click submit.] If y = Ay is a differential equation, how would the solution curves behave? A. All of the solutions curves would converge towards 0. (Stable node) B. All of the solution curves would run away from 0. (Unstable node) C. The solution curves would race towards zero and then veer away towards infinity. (Saddle) D. The solution curves converge to different points. dx dt The solution to the above differential equation with initial values x(0) = 4, y(0) = 6 is x(t) = 2e^-1.1t+2e^-4.11 y(t) e^-1.1t+50^-4.11 dy dt = -1.6x + 1y. = and the larger eigenvalue is -1.1 1.25x - 3.6y.
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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![Consider the system of differential equations
For this system, the smaller eigenvalue is -4.1
[Note--you may want to use the WolframAlpha widget (right click to open in a new window).
Enter your functions and domain, and then click submit.]
If y = Ay is a differential equation, how would the solution curves behave?
A. All of the solutions curves would converge towards 0. (Stable node)
B. All of the solution curves would run away from 0. (Unstable node)
C. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
D. The solution curves converge to different points.
dx
dt
The solution to the above differential equation with initial values x(0) = 4, y(0) = 6 is
x(t) = 2e^-1.1t+2e^-4.11
y(t) =
-1.1t+50^-4.11
dy
dt
=
-1.6x + 1y.
and the larger eigenvalue is -1.1
1.25x - 3.6y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefe48ce5-c1e8-4c52-aeb2-02053ba21519%2F349b7e06-10ca-4f20-8db7-672283daeb5b%2Flfqt7t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
For this system, the smaller eigenvalue is -4.1
[Note--you may want to use the WolframAlpha widget (right click to open in a new window).
Enter your functions and domain, and then click submit.]
If y = Ay is a differential equation, how would the solution curves behave?
A. All of the solutions curves would converge towards 0. (Stable node)
B. All of the solution curves would run away from 0. (Unstable node)
C. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
D. The solution curves converge to different points.
dx
dt
The solution to the above differential equation with initial values x(0) = 4, y(0) = 6 is
x(t) = 2e^-1.1t+2e^-4.11
y(t) =
-1.1t+50^-4.11
dy
dt
=
-1.6x + 1y.
and the larger eigenvalue is -1.1
1.25x - 3.6y.
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