(a) To determine An equation in terms of x and y such that y ( 5 ) = 1 . Explanation Given: The equation of growth rates of two species are follows: d x d t = − 4 x + 4 x y d y d t = − 3 y + 2 x y Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables, which is done as follows, ∫ d y g ( y ) = ∫ f ( x ) d x The integral of the function x n is, a follows: ∫ x n d x = x n + 1 n + 1 + c The integral of x − 1 is, ∫ 1 x d x = ln | x | + c Here, c is called the constant of integration. Calculation: The differential equations of two species are as follows: d x d t = − 4 x + 4 x y ....... ( 1 ) d y d t = − 3 y + 2 x y ....... ( 2 ) Divide equation (1) by equation (2) to obtain the value of d y d x as follows: d y d t d x d t = d y d x = − 3 y + 2 x y − 4 x + 4 x y So, the differential equation can be expressed as follows: d y d x = − 3 y + 2 x y − 4 x + 4 x y d y d x = y ( 2 x − 3 ) 4 x ( y − 1 ) Separate the variables of the above differential equations, as follows: ( y − 1 ) y d y = 2 x − 3 4 x d x Integrate the equation on both the sides (b) To determine The values of x and y such that the population of both the species becomes constant. (c) To determine The growth rate of the population from the graph when y > 1 and when y < 1 .

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.4, Problem 8E

(a)

To determine

An equation in terms of x and y such that y(5)=1.

(b)

To determine

The values of x and y such that the population of both the species becomes constant.

(c)

To determine

The growth rate of the population from the graph when y>1 and when y<1.

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Chapter 10.4, Problem 7E

Chapter 10.4, Problem 9E

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Chapter 10 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

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