The system of differential equations (dx)/(dt) = 0.5x - 0.004x^2 - 0.001xy (dy)/(dt) = 0.4y - 0.

Name: Problem 3, Chapter 9: Calculus: Early Transcendentals
Uploaded: 2020-08-24T21:24:50-08:00
Duration: 14 min 7 s
Channel: Jacquelinne S. Mejia Sandoval
Description: The system of differential equations (dx)/(dt) = 0.5x - 0.004x^2 - 0.001xy (dy)/(dt) = 0.4y - 0.001y^2 - 0.002xy is a model for the populations of two species. (a) Does the model describe cooperation, or competition, or a predator-prey relationship? (b) Find the equilibrium solutions and explain their significance.

step 1 Hello, this is problem 3. So our reference equation is DYD is equal to 0 .4y minus 0 .01Y square

Question

The system of differential equations $ \frac {dx}{dt} = 0.5x - 0.004x^2 - 0.001xy $ $ \frac {dy}{dt} = 0.4y - 0.001y^2 - 0.002xy $ is a model for the populations of two species. (a) Does the model describe cooperation, or competition, or a predator-prey relationship? (b) Find the equilibrium solutions and explain their significance.

   The system of differential equations
$ \frac {dx}{dt} = 0.5x - 0.004x^2 - 0.001xy $
$ \frac {dy}{dt} = 0.4y - 0.001y^2 - 0.002xy $
is a model for the populations of two species.
(a) Does the model describe cooperation, or competition, or a predator-prey relationship?
(b) Find the equilibrium solutions and explain their significance.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 9, Problem 3

Instant Answer

Solved by Expert Jacquelinne S. Mejia Sandoval

08/24/2020

Step 1

We can do this by examining the terms in the differential equations that involve both x and y. In both equations, the term involving both x and y is negative, which means that as one population increases, it causes the rate of change of the other population to Show more…

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The system of differential equations $ \frac {dx}{dt} = 0.5x - 0.004x^2 - 0.001xy $ $ \frac {dy}{dt} = 0.4y - 0.001y^2 - 0.002xy $ is a model for the populations of two species. (a) Does the model describe cooperation, or competition, or a predator-prey relationship? (b) Find the equilibrium solutions and explain their significance.