Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 9: First-Order Differential Equations - Section 9.5 - Systems of Equations and Phase Planes - Exercises 9.5 - Page 556: 11


The equilibrium points are $(\dfrac{c}{d},\dfrac{a}{b})$ and $(0,0)$

Work Step by Step

$\dfrac{dx}{dt}=(a-by) x$ Also, $\dfrac{dy}{dt}=(-c+dx) x$ Consider $\dfrac{dx}{dt}=0$ $(a-by) x =0 \implies y=\dfrac{a}{b}$ and $x=0$ Next, consider $\dfrac{dy}{dt}=0$ $(-c+dx) x =0 \implies x=\dfrac{c}{d}$ and $y=0$ Hence, the equilibrium points are $(\dfrac{c}{d},\dfrac{a}{b})$ and (0,0). Thus, we can see that at the equilibrium points, the rabbit or prey and foxes or, perpetrator population remains constant.
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