SOLUTIONS MANUALS
iii
,
,FUNDAMENTALS OF DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS FIFTH EDITION R. Kent Nagle
Contents
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 Differential 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...................................................................................................................................71
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
iii
, 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 Differential Equations 193
Exercises 6.1 Answers...................................................................................................... 193
Exercises 6.2 Answers...................................................................................................... 194
Exercises 6.3 Answers...................................................................................................... 194
Exercises 6.4 Answers...................................................................................................... 195
Review Problems Answers...............................................................................................196
CHAPTER 7 Laplace Transforms 197
Exercises 7.2 Detailed Solutions...................................................................................... 197
Exercises 7.3 Detailed Solutions...................................................................................... 201
iv
iii
,
,FUNDAMENTALS OF DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS FIFTH EDITION R. Kent Nagle
Contents
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 Differential 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...................................................................................................................................71
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
iii
, 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 Differential Equations 193
Exercises 6.1 Answers...................................................................................................... 193
Exercises 6.2 Answers...................................................................................................... 194
Exercises 6.3 Answers...................................................................................................... 194
Exercises 6.4 Answers...................................................................................................... 195
Review Problems Answers...............................................................................................196
CHAPTER 7 Laplace Transforms 197
Exercises 7.2 Detailed Solutions...................................................................................... 197
Exercises 7.3 Detailed Solutions...................................................................................... 201
iv
