Instructor’s Resource Manual
Differential Equations with Boundary
Value Problems
EIGHTH EDITION
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
and
A First Course in
Differential Eqautions
TENTH EDITION
Dennis Zill
Warren S. Wright
Prepared by
Warren S. Wright
Carol D. Wright
Not For Sale
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
, Not For Sale
© 2013 Brooks/Cole, Cengage Learning ISBN-13: 978-1-133-60229-3
ISBN-10: 1-133-60229-0
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Boston, MA 02210
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by the including Singapore, the United Kingdom, Australia,
license terms below. Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 To learn more about Brooks/Cole, visit
www.cengage.com/brookscole
For permission to use material from this text or product, submit
all requests online at www.cengage.com/permissions Purchase any of our products at your local college
Further permissions questions can be emailed to store or at our preferred online store
www.cengagebrain.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: any portion of the Supplement to any third party. You may not
sell, license, auction, or otherwise redistribute the Supplement in
Cengage Learning has provided you with this product (the any form. We ask that you take reasonable steps to protect the
“Supplement”) for your review and, to the extent that you adopt Supplement from unauthorized use, reproduction, or distribution.
the associated textbook for use in connection with your course Your use of the Supplement indicates your acceptance of the
(the “Course”), you and your students who purchase the conditions set forth in this Agreement. If you do not accept these
textbook may use the Supplement as described below. Cengage conditions, you must return the Supplement unused within 30
Learning has established these use limitations in response to days of receipt.
concerns raised by authors, professors, and other users
regarding the pedagogical problems stemming from unlimited All rights (including without limitation, copyrights, patents, and
distribution of Supplements. trade secrets) in the Supplement are and will remain the sole and
exclusive property of Cengage Learning and/or its licensors. The
Cengage Learning hereby grants you a nontransferable license Supplement is furnished by Cengage Learning on an “as is” basis
to use the Supplement in connection with the Course, subject to without any warranties, express or implied. This Agreement will
the following conditions. The Supplement is for your personal, be governed by and construed pursuant to the laws of the State
noncommercial use only and may not be reproduced, posted of New York, without regard to such State’s conflict of law rules.
electronically or distributed, except that portions of the
Supplement may be provided to your students IN PRINT FORM Thank you for your assistance in helping to safeguard the
ONLY in connection with your instruction of the Course, so long integrity of the content contained in this Supplement. We trust
as such students are advised that they may not copy or distribute you find the Supplement a useful teaching tool.
Printed in the United States of America
1 2 3 4 5 6 7 16 15 14 13 12
, CONTENTS
Chapter 1 Introduction To Differential Equations 1
Chapter 2 First-Order Differential Equations 30
Chapter 3 Modeling With First-Order Differential Equations 93
Chapter 4 Higher-Order Differential Equations 138
Chapter 5 Modeling With Higher-Order Differential Equations 256
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
Chapter 6 Series Solutions of Linear Equations 304
Chapter 7 The Laplace Transform 394
Chapter 8 Systems of Linear First-Order Differential Equations 472
Chapter 9 Numerical Solutions of Ordinary Differential Equations 531
Chapter 10 Plane autonomous systems 556
Chapter 11 Orthogonal functions and Fourier series 588
Chapter 12 Boundary-value Problems in R ectangular Coordinates 639
Chapter 13 Boundary-value Problems in Other Coordinate Systems 728
Chapter 14 Integral Transform method 781
Chapter 15 Numerical Solutions of Partial Differential Equations 831
A pp I 853
A pp II 855
Not For Sale
iii
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
, Not For Sale
Differential Equations with Boundary
Value Problems
EIGHTH EDITION
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
and
A First Course in
Differential Eqautions
TENTH EDITION
Dennis Zill
Warren S. Wright
Prepared by
Warren S. Wright
Carol D. Wright
Not For Sale
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
, Not For Sale
© 2013 Brooks/Cole, Cengage Learning ISBN-13: 978-1-133-60229-3
ISBN-10: 1-133-60229-0
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Channel Center Street
mechanical, including but not limited to photocopying, Boston, MA 02210
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by the including Singapore, the United Kingdom, Australia,
license terms below. Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 To learn more about Brooks/Cole, visit
www.cengage.com/brookscole
For permission to use material from this text or product, submit
all requests online at www.cengage.com/permissions Purchase any of our products at your local college
Further permissions questions can be emailed to store or at our preferred online store
www.cengagebrain.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: any portion of the Supplement to any third party. You may not
sell, license, auction, or otherwise redistribute the Supplement in
Cengage Learning has provided you with this product (the any form. We ask that you take reasonable steps to protect the
“Supplement”) for your review and, to the extent that you adopt Supplement from unauthorized use, reproduction, or distribution.
the associated textbook for use in connection with your course Your use of the Supplement indicates your acceptance of the
(the “Course”), you and your students who purchase the conditions set forth in this Agreement. If you do not accept these
textbook may use the Supplement as described below. Cengage conditions, you must return the Supplement unused within 30
Learning has established these use limitations in response to days of receipt.
concerns raised by authors, professors, and other users
regarding the pedagogical problems stemming from unlimited All rights (including without limitation, copyrights, patents, and
distribution of Supplements. trade secrets) in the Supplement are and will remain the sole and
exclusive property of Cengage Learning and/or its licensors. The
Cengage Learning hereby grants you a nontransferable license Supplement is furnished by Cengage Learning on an “as is” basis
to use the Supplement in connection with the Course, subject to without any warranties, express or implied. This Agreement will
the following conditions. The Supplement is for your personal, be governed by and construed pursuant to the laws of the State
noncommercial use only and may not be reproduced, posted of New York, without regard to such State’s conflict of law rules.
electronically or distributed, except that portions of the
Supplement may be provided to your students IN PRINT FORM Thank you for your assistance in helping to safeguard the
ONLY in connection with your instruction of the Course, so long integrity of the content contained in this Supplement. We trust
as such students are advised that they may not copy or distribute you find the Supplement a useful teaching tool.
Printed in the United States of America
1 2 3 4 5 6 7 16 15 14 13 12
, CONTENTS
Chapter 1 Introduction To Differential Equations 1
Chapter 2 First-Order Differential Equations 30
Chapter 3 Modeling With First-Order Differential Equations 93
Chapter 4 Higher-Order Differential Equations 138
Chapter 5 Modeling With Higher-Order Differential Equations 256
© Cengage Learning. All rights reserved. No distribution allowed without express authorization.
Chapter 6 Series Solutions of Linear Equations 304
Chapter 7 The Laplace Transform 394
Chapter 8 Systems of Linear First-Order Differential Equations 472
Chapter 9 Numerical Solutions of Ordinary Differential Equations 531
Chapter 10 Plane autonomous systems 556
Chapter 11 Orthogonal functions and Fourier series 588
Chapter 12 Boundary-value Problems in R ectangular Coordinates 639
Chapter 13 Boundary-value Problems in Other Coordinate Systems 728
Chapter 14 Integral Transform method 781
Chapter 15 Numerical Solutions of Partial Differential Equations 831
A pp I 853
A pp II 855
Not For Sale
iii
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed
with a certain product or service or otherwise on a password-protected website for classroom use.
, Not For Sale
