dx dt dy dt || -1.6x + 0.5y, 2.5x - 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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Need only a handwritten solution only (not a typed one).
![Consider the system of differential equations
For this system, the smaller eigenvalue is
dx
dt
dy
dt
-1.6x +0.5y,
2.5x - 3.6y.
and the larger eigenvalue is
[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?
O A. The solution curves converge to different points.
OB. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
O C. All of the solutions curves would converge towards 0. (Stable node)
D. All of the solution curves would run away from 0. (Unstable node)
The solution to the above differential equation with initial values ï(0) = 3, y(0) = 3 is
x(t) =
y(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2afdbd03-1d4f-410f-be1f-3d702a57a84b%2F9258a9e8-988a-4e24-90f2-49e5a806295c%2Fyskg7cq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
For this system, the smaller eigenvalue is
dx
dt
dy
dt
-1.6x +0.5y,
2.5x - 3.6y.
and the larger eigenvalue is
[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?
O A. The solution curves converge to different points.
OB. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
O C. All of the solutions curves would converge towards 0. (Stable node)
D. All of the solution curves would run away from 0. (Unstable node)
The solution to the above differential equation with initial values ï(0) = 3, y(0) = 3 is
x(t) =
y(t) =
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