Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 1 - Introduction - 1.1 Some Basic Mathematical Models; Direction Fields - Problems - Page 8: 20



Work Step by Step

The directional field for question 19 shows a field with an equilibrium solution at $y=3$ and another at $y=0$; it converges as $t →∞$, for $y_0\gt0$, to $y=3$. For $y_0\lt0$, $y→-∞$. Because there are two equilibrium solutions, it can be inferred that the differential equation is not of the form $\frac{dy}{dt}=(a+by)^n$, this is because equations in this form can have a single equilibrium solution. This rules out answers (a), (b), (c), (f), (g), (i)and (j). All remaining answer choices are of the form $\frac{dy}{dt}=(a+by)(c+dy)$. Answer choice (d) does not have an equilibrium solution at $y=3$, so it is ruled out. The answer is either (e) or (h). Since the field is divergent for $y_0\gt3$, this must mean that $y′\gt0$ for this space; this is only true for answer choice (e).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.