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INSTRUCTOR’S SOLUTIONS MANUAL
FUNDAMENTALS OF DIFFERENTIAL EQUATIONS
SEVENTH EDITION

AND FUNDAMENTALS OF DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS
FIFTH EDITION

R. Kent Nagle
University of South Florida

Edward B. Saff
Vanderbilt University

A. David Snider
University of South Florida

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This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available tostudents except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright © 2008 Pearson Education, Inc. Publishing asPearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. ISBN-13: 978-0-321-38844-5 ISBN-10: 0-321-38844-5

Contents
Notes to theInstructor
Software Supplements . . . . . . . . . . . . . Computer Labs . . . . . . . . . . . . . . . . Group Projects . . . . . . . . . . . . . . . . . Technical Writing Exercises . . . . . . . . . . Student Presentations . . . . . . . . . . . . . Homework Assignments . . . . . . . . . . . . Syllabus Suggestions . . . . . . . . . . . . . . Numerical, Graphical, and Qualitative MethodsEngineering/Physics Applications . . . . . . Biology/Ecology Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 2 2 2 3 3 4 5 7 9 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 17 18 22 25 28 29 35 35 41 48 56 61 70 71 71 iii

Supplemental Group Projects Detailed Solutions & Answers to Even-Numbered Problems
CHAPTER 1 Introduction Exercises 1.1 Detailed Solutions . Exercises 1.2 Detailed Solutions . Exercises 1.3 DetailedSolutions . Exercises 1.4 Detailed Solutions . Tables . . . . . . . . . . . . . . . . Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 2 First Order Differential Equations Exercises 2.2 Detailed Solutions . . . . . . . . . . . Exercises 2.3 Detailed Solutions . . . . . . . . . . . Exercises 2.4 Detailed Solutions . . . . . . . . . . . Exercises2.5 Detailed Solutions . . . . . . . . . . . Exercises 2.6 Detailed Solutions . . . . . . . . . . . Review Problems Answers . . . . . . . . . . . . . . Tables . . . . . . . . . . . . . . . . . . . . . . . . . . Figures . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 3

Mathematical Models and Numerical Methods Involving First Order Equations Exercises 3.2 Detailed Solutions . . ....