Differential Equations for Dummies - Softouch

1 By Steven Holzner, PhDDifferentialEquationsFORDUMmIES 4/28/08 11:27 PM Page 4/28/08 11:27 PM Page iiDifferentialEquationsFORDUMmIES 4/28/08 11:27 PM Page 4/28/08 11:27 PM Page iiby Steven Holzner, PhDDifferentialEquationsFORDUMmIES 4/28/08 11:27 PM Page iiiDifferential Equations For Dummies Published byWiley Publishing, River , NJ 2008 by Wiley Publishing, Inc., Indianapolis, IndianaPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any formor by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as per-mitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior writtenpermission of the Publisher, or authorization through payment of the appropriate per-copy fee to theCopyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923.

2 978-750-8400, fax to the Publisher for permission should be addressed to the Legal Department, Wiley Publishing,Inc., 10475 Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4355, or online : Wiley, the Wiley Publishing logo, For Dummies , the Dummies Man logo, A Reference for theRest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, and related tradedress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the UnitedStates and other countries, and may not be used without written permission.

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5 Please contact our Customer CareDepartment within the at 800-762-2974, outside the at 317-572-3993, or fax technical support, please visit also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic of Congress Control Number: 2008925781 ISBN: 978-0-470-17814-0 Manufactured in the United States of America10 9 8 7 6 5 4 3 2 4/28/08 11:27 PM Page ivAbout the AuthorSteven Holzneris an award-winning author of science, math, and technicalbooks. He got his training in Differential Equations at MIT and at CornellUniversity, where he got his PhD.

6 He has been on the faculty at both MIT andCornell University, and has written such bestsellers as physics For Dummiesand physics Workbook For 4/28/08 11:27 PM Page 4/28/08 11:27 PM Page viDedicationTo Nancy, always and s AcknowledgmentsThe book you hold in your hands is the work of many people. I d especiallylike to thank Tracy Boggier, Georgette Beatty, Jessica Smith, technicalreviewer Jamie Song, PhD, and the folks in Composition Services who put thebook together so 4/28/08 11:27 PM Page viiPublisher s AcknowledgmentsWe re proud of this book.

7 Please send us your comments through our Dummies online registrationform located at of the people who helped bring this book to market include the following:Acquisitions, Editorial, and Media DevelopmentProject Editor: Georgette BeattyAcquisitions Editor: Tracy BoggierCopy Editor: Jessica SmithEditorial Program Coordinator:Erin Calligan MooneyTechnical Editor: Jamie Song, PhDEditorial Manager: Michelle HackerEditorial Assistants:Joe Niesen, Leeann HarneyCartoons: Rich Tennant( )Composition ServicesProject Coordinator:Erin SmithLayout and Graphics:Carrie A.

8 Cesavice,Stephanie D. JumperProofreaders:Caitie Kelly, Linda D. MorrisIndexer:Broccoli Information ManagementPublishing and Editorial for Consumer DummiesDiane Graves Steele, Vice President and Publisher, Consumer DummiesJoyce Pepple, Acquisitions Director, Consumer DummiesKristin A. Cocks, Product Development Director, Consumer DummiesMichael Spring, Vice President and Publisher, TravelKelly Regan,Editorial Director, TravelPublishing for Technology DummiesAndy Cummings,Vice President and Publisher, Dummies Technology/General UserComposition ServicesGerry Fahey,Vice President of Production ServicesDebbie Stailey,Director of Composition 4/28/08 11:27 PM Page viiiContents at a GlanceIntroduction.

9 1 Part I: Focusing on First Order Differential 1: Welcome to the World of Differential Equations ..7 Chapter 2: Looking at Linear First Order Differential 3: Sorting Out Separable First Order Differential 4: Exploring Exact First Order Differential Equations and Euler s II: Surveying Second and Higher OrderDifferential Equations ..89 Chapter 5: Examining Second Order Linear Homogeneous Differential Equations ..91 Chapter 6: Studying Second Order Linear Nonhomogeneous Differential Equations ..123 Chapter 7: Handling Higher Order Linear Homogeneous Differential Equations .

10 151 Chapter 8: Taking On Higher Order Linear Nonhomogeneous Differential Equations ..173 Part III: The Power Stuff: Advanced Techniques ..189 Chapter 9: Getting Serious with Power Series and Ordinary 10: Powering through Singular Points ..213 Chapter 11: Working with Laplace Transforms ..239 Chapter 12: Tackling Systems of First Order Linear Differential Equations ..265 Chapter 13: Discovering Three Fail-Proof Numerical Methods ..293 Part IV: The Part of Tens ..315 Chapter 14: Ten Super-Helpful Online Differential Equation 15: Ten Really Cool Online Differential Equation Solving Tools.