Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(1) and y(t) can be modeled by the equations dx dt = 1.4x -0.75y, dy dt For this system, the smaller eigenvalue is 0.9 3.9 = -1.66666666666667x + 3.4y. and the larger eigenvalue is The solution to the above differential equation with initial values x(0) = 7, y(0) = 7 is x(t) = y(t) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the interaction of two species of animals in a habitat. We are told that the change of the populations
x(t) and y(t) can be modeled by the equations
dx
dt
=
dy
dt
For this system, the smaller eigenvalue is 0.9
3.9
1.4x -0.75y,
-1.66666666666667x + 3.4y.
and the larger eigenvalue is
The solution to the above differential equation with initial values x(0) = 7, y(0) = 7 is
x(t) =
I
y(t) =
Transcribed Image Text:Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by the equations dx dt = dy dt For this system, the smaller eigenvalue is 0.9 3.9 1.4x -0.75y, -1.66666666666667x + 3.4y. and the larger eigenvalue is The solution to the above differential equation with initial values x(0) = 7, y(0) = 7 is x(t) = I y(t) =
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