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Get Full Access to Numerical Analysis - 10 Edition - Chapter 5.9 - Problem 6
Get Full Access to Numerical Analysis - 10 Edition - Chapter 5.9 - Problem 6

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# In Exercise 5, we considered the problem of predicting the population in a predator-prey ISBN: 9781305253667 457

## Solution for problem 6 Chapter 5.9

Numerical Analysis | 10th Edition

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Problem 6

In Exercise 5, we considered the problem of predicting the population in a predator-prey model. Another problem of this type is concerned with two species competing for the same food supply. If the numbers ofspecies alive attime t are denoted by X| (/) and *2(0, it is often assumed that, although the birthrate of each of the species is simply proportional to the number ofspecies alive at that time, the death rate of each species depends on the population of both species. We will assume that the population of a particular pair of species is described by the equations d ^ll = Xl (f )[4 - 0.0003xi(t) - 0.0004x2(0] and dt dX2(t) = X2(Ot2 - 0.0002xi(0 - 0.0001x2(0]. dt If it is known that the initial population of each species is 10,000, find the solution to this system for 0 < t < 4. Is there a stable solution to this population model? If so, for what values of x\ and X2 is the solution stable?

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th Math 340 Lecture – Introduction to Ordinary Differential Equations – April 18 , 2016 What We Covered: 1. Course Content – Chapter 9: Linear Systems with Constant Coefficients a. Section 9.9: Inhomogeneous Linear Systems i. Definition: You’re given the linear equation = + () where f(t) is the inhomogeneous term because it’s not dependent on y ii. Theorem: Suppose that y is p particular solution to the inhomogeneous equation and that 1 2..., frm a fundamental set of solutions to the associated ′ homogeneous equation =

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##### ISBN: 9781305253667

The full step-by-step solution to problem: 6 from chapter: 5.9 was answered by , our top Math solution expert on 03/16/18, 03:24PM. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. Since the solution to 6 from 5.9 chapter was answered, more than 236 students have viewed the full step-by-step answer. Numerical Analysis was written by and is associated to the ISBN: 9781305253667. The answer to “In Exercise 5, we considered the problem of predicting the population in a predator-prey model. Another problem of this type is concerned with two species competing for the same food supply. If the numbers ofspecies alive attime t are denoted by X| (/) and *2(0, it is often assumed that, although the birthrate of each of the species is simply proportional to the number ofspecies alive at that time, the death rate of each species depends on the population of both species. We will assume that the population of a particular pair of species is described by the equations d ^ll = Xl (f )[4 - 0.0003xi(t) - 0.0004x2(0] and dt dX2(t) = X2(Ot2 - 0.0002xi(0 - 0.0001x2(0]. dt If it is known that the initial population of each species is 10,000, find the solution to this system for 0 < t < 4. Is there a stable solution to this population model? If so, for what values of x\ and X2 is the solution stable?” is broken down into a number of easy to follow steps, and 166 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 1204 solutions.

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