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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 INSTRUCTORS SOLUTIONS MANUAL 388445Naglettl.qxd 1/9/08 11:53 AM Page 1 2. Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright 2008 Pearson Education, Inc.
Publishing as Pearson 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 trans- mitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, with- out the prior written permission of the publisher. ISBN-13: 978-0-321-38844-5 ISBN-10: 0-321-38844-5 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 permit- ted.The work and materials from it should never be made available to students 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. 388445Naglettl.qxd 1/9/08 11:53 AM Page 2 3. Contents Notes to the Instructor 1 Software Supplements. 1 Computer Labs.
1 Group Projects. 2 Technical Writing Exercises. 2 Student Presentations. 2 Homework Assignments.
3 Syllabus Suggestions. 3 Numerical, Graphical, and Qualitative Methods.
4 Engineering/Physics Applications. 5 Biology/Ecology Applications.
7 Supplemental Group Projects 9 Detailed Solutions & Answers to Even-Numbered Problems 17 CHAPTER 1 Introduction 17 Exercises 1.1 Detailed Solutions. 17 Exercises 1.2 Detailed Solutions. 18 Exercises 1.3 Detailed Solutions. 22 Exercises 1.4 Detailed Solutions.
25 Tables. 28 Figures. 29 CHAPTER 2 First Order Dierential Equations 35 Exercises 2.2 Detailed Solutions.
35 Exercises 2.3 Detailed Solutions. 41 Exercises 2.4 Detailed Solutions.
48 Exercises 2.5 Detailed Solutions. 56 Exercises 2.6 Detailed Solutions.
61 Review Problems Answers. 70 Tables. 71 Figures. CHAPTER 3 Mathematical Models and Numerical Methods Involving First Order Equations 73 Exercises 3.2 Detailed Solutions. 73 Exercises 3.3 Detailed Solutions. 81 Exercises 3.4 Detailed Solutions.
87 Exercises 3.5 Answers. 96 Exercises 3.6 Answers.
97 Exercises 3.7 Answers. 97 Tables. 98 Figures. 100 CHAPTER 4 Linear Second Order Equations 101 Exercises 4.1 Detailed Solutions. 101 Exercises 4.2 Detailed Solutions. 103 Exercises 4.3 Detailed Solutions.
111 Exercises 4.4 Detailed Solutions. 119 Exercises 4.5 Detailed Solutions. 125 Exercises 4.6 Detailed Solutions.
137 Exercises 4.7 Detailed Solutions. 144 Exercises 4.8 Detailed Solutions. 157 Exercises 4.9 Detailed Solutions. 160 Exercises 4.10 Detailed Solutions. 167 Review Problems Answers. 172 Figures.
173 CHAPTER 5 Introduction to Systems and Phase Plane Analysis 177 Exercises 5.2 Answers. 177 Exercises 5.3 Answers. 179 Exercises 5.4 Answers. 180 Exercises 5.5 Answers. 182 Exercises 5.6 Answers. 182 Exercises 5.7 Answers. 183 Exercises 5.8 Answers.
183 Review Problems Answers. 184 Tables. 185 Figures.
187 CHAPTER 6 Theory of Higher-Order Linear Dierential Equations 193 Exercises 6.1 Answers. 193 Exercises 6.2 Answers. 194 Exercises 6.3 Answers. 194 Exercises 6.4 Answers.
Review Problems Answers. 196 CHAPTER 7 Laplace Transforms 197 Exercises 7.2 Detailed Solutions.
197 Exercises 7.3 Detailed Solutions. 201 Exercises 7.4 Detailed Solutions. 206 Exercises 7.5 Detailed Solutions. 215 Exercises 7.6 Detailed Solutions. 224 Exercises 7.7 Detailed Solutions. 239 Exercises 7.8 Detailed Solutions. 247 Exercises 7.9 Detailed Solutions.
252 Review Problems Answers. 262 Figures.
263 CHAPTER 8 Series Solutions of Dierential Equations 267 Exercises 8.1 Answers. 267 Exercises 8.2 Answers. 268 Exercises 8.3 Answers.
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269 Exercises 8.4 Answers. 270 Exercises 8.5 Answers. 271 Exercises 8.6 Answers. 271 Exercises 8.7 Answers.
273 Exercises 8.8 Answers. 274 Review Problems Answers. 275 Figures. 276 CHAPTER 9 Matrix Methods for Linear Systems 277 Exercises 9.1 Answers. 277 Exercises 9.2 Answers. 277 Exercises 9.3 Answers.
278 Exercises 9.4 Answers. 280 Exercises 9.5 Answers. 282 Exercises 9.6 Answers. 285 Exercises 9.7 Answers. 286 Exercises 9.8 Answers.
287 Review Problems Answers. 289 Figures. 290 CHAPTER 10 Partial Dierential Equations 291 Exercises 10.2 Answers.
291 Exercises 10.3 Answers. 291 Exercises 10.4 Answers. Exercises 10.5 Answers.
293 Exercises 10.6 Answers. 294 Exercises 10.7 Answers. 295 CHAPTER 11 Eigenvalue Problems and Sturm-Liouville Equations 297 Exercises 11.2 Answers. 297 Exercises 11.3 Answers. 298 Exercises 11.4 Answers. 298 Exercises 11.5 Answers. 299 Exercises 11.6 Answers.
300 Exercises 11.7 Answers. 302 Exercises 11.8 Answers. 303 Review Problems Answers.
303 CHAPTER 12 Stability of Autonomous Systems 305 Exercises 12.2 Answers. 305 Exercises 12.3 Answers. 305 Exercises 12.4 Answers.
306 Exercises 12.5 Answers. 306 Exercises 12.6 Answers. 307 Exercises 12.7 Answers. 307 Review Problems Answers. 308 Figures. 309 CHAPTER 13 Existence and Uniqueness Theory 317 Exercises 13.1 Answers. 317 Exercises 13.2 Answers.
317 Exercises 13.3 Answers. 318 Exercises 13.4 Answers. 318 Review Problems Answers.
Notes to the Instructor One goal in our writing has been to create exible texts that aord the instructor a variety of topics and make available to the student an abundance of practice problems and projects. We recommend that the instructor read the discussion given in the preface in order to gain an overview of the prerequisites, topics of emphasis, and general philosophy of the text.
Software Supplements Interactive Dierential Equations CD-ROM: By Beverly West (Cornell University), Steven Strogatz (Cornell University), Jean Marie McDill (California Polytechnic State Uni- versity San Luis Obispo), John Cantwell (St. Louis University), and Hubert Hohn (Mas- sachusetts College of Arts) is a popular software directly tied to the text that focuses on helping students visualize concepts. Applications are drawn from engineering, physics, chemistry, and biology. Runs on Windows or Macintosh and is included free with every book. Instructors MAPLE/MATHLAB/MATHEMATICA manual: By Thomas W.
Po- laski (Winthrop University), Bruno Welfert (Arizona State University), and Maurino Bautista (Rochester Institute of Technology). A collection of worksheets and projects to aid instruc- tors in integrating computer algebra systems into their courses. Available via Addison-Wesley Instructors Resource Center.
MATLAB Manual ISBN 13: 978-0-321-53015-8; ISBN 10: 0-321-53015-2 MAPLE Manual ISBN 13: 978-0-321-38842-1; ISBN 10: 0-321-38842-9 MATHEMATICA Manual ISBN 13: 978-0-321-52178-1; ISBN 10: 0-321-52178-1 Computer Labs A computer lab in connection with a dierential equations course can add a whole new di- mension to the teaching and learning of dierential equations. As more and more colleges and universities set up computer labs with software such as MAPLE, MATLAB, DERIVE, MATHEMATICA, PHASEPLANE, and MACMATH, there will be more opportunities to in- clude a lab as part of the dierential equations course. In our teaching and in our texts, we have tried to provide a variety of exercises, problems, and projects that encourage the student to use the computer to explore. Even one or two hours at a computer generating phase plane diagrams can provide the students with a feeling of how they will use technology together 1 8. With the theory to investigate real world problems. Furthermore, our experience is that they thoroughly enjoy these activities.
Of course, the software, provided free with the texts, is especially convenient for such labs. Group Projects Although the projects that app.