The system of differential equations 1 da x dt model the interaction of two populations & and y. (a) What kind of interaction do these equations describe? predator-prey y-1-0.05x, 1 dy y dt = 1- x -0.05y (Symbiosis takes place when the interaction of two species benefits both. An example is the pollination of plants by insects.) (b) Now suppose that we start with the initial populations (2(0), y(0)) = (1.5, 3). What happens to the populations in the long run? The population à oscillates The population y oscillates (To answer this question you will want to use a calculator or computer to draw slope fields.)
The system of differential equations 1 da x dt model the interaction of two populations & and y. (a) What kind of interaction do these equations describe? predator-prey y-1-0.05x, 1 dy y dt = 1- x -0.05y (Symbiosis takes place when the interaction of two species benefits both. An example is the pollination of plants by insects.) (b) Now suppose that we start with the initial populations (2(0), y(0)) = (1.5, 3). What happens to the populations in the long run? The population à oscillates The population y oscillates (To answer this question you will want to use a calculator or computer to draw slope fields.)
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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Transcribed Image Text:The system of differential equations
1 da
x dt
y-1-0.05x,
model the interaction of two populations and y.
(a) What kind of interaction do these equations describe?
predator-prey
1 dy
y dt
= 1- x -0.05y
(Symbiosis takes place when the interaction of two species benefits both. An example is the pollination of plants by insects.)
(b) Now suppose that we start with the initial populations (x(0), y(0)) = (1.5, 3). What happens to the populations in the
long run?
The population a oscillates
The population y oscillates
(To answer this question you will want to use a calculator or computer to draw slope fields.)
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