Solutions Manual for
Fundamentals of Differential
Equations 9th Global Edition By
Kent Nagle, Edward Saff, Arthur
David Snider
(All Chapters 1-10, 100% Original
Verified, A+ Grade)
This is The Only Original and
Complete Test Bank for 10th
Edition, All Other Files in The
Market are Fake/Old/Wrong
Edition.
Part 1: Even Number Solutions
Part 2: Odd Number Solutions
, Table of Contents
1. Introduction
2. First-Order Differential Equations
3. Mathematical Models and Numerical
Methods Involving First Order Equations
4. Linear Second-Order Equations
5. Introduction to Systems and Phase
Plane Analysis
6. Theory of Higher-Order Linear
Differential Equations
7. Laplace Transforms
8. Series Solutions of Differential
Equations
9. Matrix Methods for Linear Systems
10. Partial Differential Equations
, Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
Part 1: Even Number Answers
Contents
Notes to the Instructor 1
Supplements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Computer Labs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Group Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Technical Writing Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Student Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Homework Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Syllabus Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Numerical, Graphical, and Qualitative Methods . . . . . . . . . . . . . . . . . . 3
Engineering/Physics Applications . . . . . . . . . . . . . . . . . . . . . . . . . 5
Biology/Ecology Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Economics Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Supplemental Group Projects 10
Detailed Solutions & Answers to Even-Numbered Problems 23
CHAPTER 1 Introduction 23
Exercises 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Exercises 1.2 Solutions and Initial Value Problems . . . . . . . . . . . . . . . 24
Exercises 1.3 Direction Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Exercises 1.4 The Approximation Method of Euler . . . . . . . . . . . . . . . 31
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
CHAPTER 2 First Order Differential Equations 43
Exercises 2.2 Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . 43
Exercises 2.3 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Exercises 2.4 Exact Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Exercises 2.5 Special Integrating Factors . . . . . . . . . . . . . . . . . . . . 66
Exercises 2.6 Substitutions and Transformations . . . . . . . . . . . . . . . . 72
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Copyright c 2019 Pearson Education Ltd. i
Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
, Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
ii Contents
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
CHAPTER 3 Mathematical Models and Numerical Methods
Involving First Order Equations 85
Exercises 3.2 Compartmental Analysis . . . . . . . . . . . . . . . . . . . . . 85
Exercises 3.3 Heating and Cooling of Buildings . . . . . . . . . . . . . . . . . 93
Exercises 3.4 Newtonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . 99
Exercises 3.5 Electrical Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 108
Exercises 3.6 Improved Euler’s Method . . . . . . . . . . . . . . . . . . . . . 109
Exercises 3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta . . 109
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
CHAPTER 4 Linear Second Order Equations 113
Exercises 4.1 Introduction: The Mass-Spring Oscillator . . . . . . . . . . . . 113
Exercises 4.2 Homogeneous Linear Equations: The General Solution . . . . . 115
Exercises 4.3 Auxiliary Equations with Complex Roots . . . . . . . . . . . . 123
Exercises 4.4 Nonhomogeneous Equations: The Method of Undetermined
Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Exercises 4.5 The Superposition Principle and Undetermined Coefficients
Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Exercises 4.6 Variation of Parameters . . . . . . . . . . . . . . . . . . . . . . 148
Exercises 4.7 Variable-Coefficient Equations . . . . . . . . . . . . . . . . . . 156
Exercises 4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Exercises 4.9 A Closer Look at Free Mechanical Vibrations . . . . . . . . . . 172
Exercises 4.10 A Closer Look at Forced Mechanical Vibrations . . . . . . . . 178
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
CHAPTER 5 Introduction to Systems and Phase Plane Analysis 191
Exercises 5.2 Elimination Method for Systems with Constant Coefficients . . 191
Exercises 5.3 Solving Systems and Higher–Order Equations Numerically . . . 193
Exercises 5.4 Introduction to the Phase Plane . . . . . . . . . . . . . . . . . 194
Exercises 5.5 Applications to Biomathematics: Epidemic and Tumor Growth
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Exercises 5.6 Coupled Mass–Spring Systems . . . . . . . . . . . . . . . . . . 196
Exercises 5.7 Electrical Systems . . . . . . . . . . . . . . . . . . . . . . . . . 196
Exercises 5.8 Dynamical Systems, Poincarè Maps, and Chaos . . . . . . . . . 197
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Copyright c 2019 Pearson Education Ltd.
Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
Fundamentals of Differential
Equations 9th Global Edition By
Kent Nagle, Edward Saff, Arthur
David Snider
(All Chapters 1-10, 100% Original
Verified, A+ Grade)
This is The Only Original and
Complete Test Bank for 10th
Edition, All Other Files in The
Market are Fake/Old/Wrong
Edition.
Part 1: Even Number Solutions
Part 2: Odd Number Solutions
, Table of Contents
1. Introduction
2. First-Order Differential Equations
3. Mathematical Models and Numerical
Methods Involving First Order Equations
4. Linear Second-Order Equations
5. Introduction to Systems and Phase
Plane Analysis
6. Theory of Higher-Order Linear
Differential Equations
7. Laplace Transforms
8. Series Solutions of Differential
Equations
9. Matrix Methods for Linear Systems
10. Partial Differential Equations
, Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
Part 1: Even Number Answers
Contents
Notes to the Instructor 1
Supplements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Computer Labs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Group Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Technical Writing Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Student Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Homework Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Syllabus Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Numerical, Graphical, and Qualitative Methods . . . . . . . . . . . . . . . . . . 3
Engineering/Physics Applications . . . . . . . . . . . . . . . . . . . . . . . . . 5
Biology/Ecology Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Economics Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Supplemental Group Projects 10
Detailed Solutions & Answers to Even-Numbered Problems 23
CHAPTER 1 Introduction 23
Exercises 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Exercises 1.2 Solutions and Initial Value Problems . . . . . . . . . . . . . . . 24
Exercises 1.3 Direction Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Exercises 1.4 The Approximation Method of Euler . . . . . . . . . . . . . . . 31
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
CHAPTER 2 First Order Differential Equations 43
Exercises 2.2 Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . 43
Exercises 2.3 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Exercises 2.4 Exact Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Exercises 2.5 Special Integrating Factors . . . . . . . . . . . . . . . . . . . . 66
Exercises 2.6 Substitutions and Transformations . . . . . . . . . . . . . . . . 72
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Copyright c 2019 Pearson Education Ltd. i
Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
, Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
ii Contents
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
CHAPTER 3 Mathematical Models and Numerical Methods
Involving First Order Equations 85
Exercises 3.2 Compartmental Analysis . . . . . . . . . . . . . . . . . . . . . 85
Exercises 3.3 Heating and Cooling of Buildings . . . . . . . . . . . . . . . . . 93
Exercises 3.4 Newtonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . 99
Exercises 3.5 Electrical Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 108
Exercises 3.6 Improved Euler’s Method . . . . . . . . . . . . . . . . . . . . . 109
Exercises 3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta . . 109
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
CHAPTER 4 Linear Second Order Equations 113
Exercises 4.1 Introduction: The Mass-Spring Oscillator . . . . . . . . . . . . 113
Exercises 4.2 Homogeneous Linear Equations: The General Solution . . . . . 115
Exercises 4.3 Auxiliary Equations with Complex Roots . . . . . . . . . . . . 123
Exercises 4.4 Nonhomogeneous Equations: The Method of Undetermined
Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Exercises 4.5 The Superposition Principle and Undetermined Coefficients
Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Exercises 4.6 Variation of Parameters . . . . . . . . . . . . . . . . . . . . . . 148
Exercises 4.7 Variable-Coefficient Equations . . . . . . . . . . . . . . . . . . 156
Exercises 4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Exercises 4.9 A Closer Look at Free Mechanical Vibrations . . . . . . . . . . 172
Exercises 4.10 A Closer Look at Forced Mechanical Vibrations . . . . . . . . 178
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
CHAPTER 5 Introduction to Systems and Phase Plane Analysis 191
Exercises 5.2 Elimination Method for Systems with Constant Coefficients . . 191
Exercises 5.3 Solving Systems and Higher–Order Equations Numerically . . . 193
Exercises 5.4 Introduction to the Phase Plane . . . . . . . . . . . . . . . . . 194
Exercises 5.5 Applications to Biomathematics: Epidemic and Tumor Growth
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Exercises 5.6 Coupled Mass–Spring Systems . . . . . . . . . . . . . . . . . . 196
Exercises 5.7 Electrical Systems . . . . . . . . . . . . . . . . . . . . . . . . . 196
Exercises 5.8 Dynamical Systems, Poincarè Maps, and Chaos . . . . . . . . . 197
Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Copyright c 2019 Pearson Education Ltd.
Solutions Manual for Fundamentals of Differential Equations 9th Global Edition By Kent Nagle, Edward Saff, Arthur David Snider
