# Elementary Differential Equations and Boundary Value Problems 10th edition

William Boyce and Richard DiPrima
Publisher: John Wiley & Sons

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• Chapter 1: Introduction
• 1.1: Some Basic Mathematical Models; Direction Fields (23)
• 1.2: Solutions of Some Differential Equations (16)
• 1.3: Classification of Differential Equations (25)
• 1.4: Historical Remarks

• Chapter 2: First Order Differential Equations
• 2.1: Linear Equations; Method of Integrating Factors (18)
• 2.2: Separable Equations (15)
• 2.3: Modeling with First Order Equations (15)
• 2.4: Differences Between Linear and Nonlinear Equations (14)
• 2.5: Autonomous Equations and Population Dynamics (7)
• 2.6: Exact Equations and Integrating Factors (16)
• 2.7: Numerical Approximations: Euler's Method (15)
• 2.8: The Existence and Uniqueness Theorem (10)
• 2.9: First Order Difference Equations (6)
• 2.M: Miscellaneous Problems

• Chapter 3: Second Order Linear Equations
• 3.1: Homogeneous Equations with Constant Coefficients (15)
• 3.2: Solutions of Linear Homogeneous Equations; the Wronskian (21)
• 3.3: Complex Roots of the Characteristic Equations (17)
• 3.4: Repeated Roots; Reduction of Order (19)
• 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients (19)
• 3.6: Variation of Parameters (16)
• 3.7: Mechanical and Electrical Vibrations (15)
• 3.8: Forced Vibrations (15)

• Chapter 4: Higher Order Linear Equations
• 4.1: General Theory of nth Order Linear Equations (17)
• 4.2: Homogeneous Equations with Constant Coefficients (20)
• 4.3: The Method of Undetermined Coefficients (15)
• 4.4: The Method of Variation of Parameters (12)

• Chapter 5: Series Solutions of Second Order Linear Equations
• 5.1: Review of Power Series (17)
• 5.2: Series Solutions Near an Ordinary Point, Part I (11)
• 5.3: Series Solutions Near an Ordinary Point, Part II (16)
• 5.4: Euler Equations; Regular Singular Points (23)
• 5.5: Series Solutions Near a Regular Singular Point, Part I (10)
• 5.6: Series Solutions Near a Regular Singular Point, Part II (12)
• 5.7: Bessel's Equation (4)

• Chapter 6: The Laplace Transform
• 6.1: Definition of the Laplace Transform (17)
• 6.2: Solution of Initial Value Problems (18)
• 6.3: Step Functions (17)
• 6.4: Differential Equations with Discontinuous Forcing Functions (14)
• 6.5: Impulse Functions (11)
• 6.6: The Convolution Integral (16)

• Chapter 7: Systems of First Order Linear Equations
• 7.1: Introduction (13)
• 7.2: Review of Matrices (14)
• 7.3: Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors (15)
• 7.4: Basic Theory of Systems of First Order Linear Equations (3)
• 7.5: Homogeneous Linear Systems with Constant Coefficients (15)
• 7.6: Complex Eigenvalues (15)
• 7.7: Fundamental Matrices (12)
• 7.8: Repeated Eigenvalues (9)
• 7.9: Nonhomogeneous Linear Systems (13)

• Chapter 8: Numerical Methods
• 8.1: The Euler or Tangent Line Method (14)
• 8.2: Improvements on the Euler Method (15)
• 8.3: The Runge–Kutta Method (11)
• 8.4: Multistep Methods (5)
• 8.5: Systems of First Order Equations (4)
• 8.6: More on Errors; Stability (2)

• Chapter 9: Nonlinear Differential Equations and Stability
• 9.1: The Phase Plane: Linear Systems (11)
• 9.2: Autonomous Systems and Stability (12)
• 9.3: Locally Linear Systems (10)
• 9.4: Competing Species (10)
• 9.5: Predator–Prey Equations (9)
• 9.6: Liapunov's Second Method (3)
• 9.7: Periodic Solutions and Limit Cycles (7)
• 9.8: Chaos and Strange Attractors: The Lorentz Equations (8)

• Chapter 10: Partial Differential Equations and Fourier Series
• 10.1: Two-Point Boundary Value Problems (16)
• 10.2: Fourier Series (17)
• 10.3: The Fourier Convergence Theorem (11)
• 10.4: Even and Odd Functions (17)
• 10.5: Separation of Variables; Heat Conduction in a Rod (12)
• 10.6: Other Heat Conduction Problems (13)
• 10.7: The Wave Equation: Vibrations of an Elastic String (10)
• 10.8: Laplace's Equation (11)

• Chapter 11: Boundary Value Problems and Sturm-Liouville Theory
• 11.1: The Occurrence of Two-Point Boundary Value Problems (15)
• 11.2: Sturm–Liouville Boundary Value Problems (18)
• 11.3: Nonhomogeneous Boundary Value Problems (18)
• 11.4: Singular Sturm–Liouville Problems (1)
• 11.5: Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion (2)
• 11.6: Series of Orthogonal Functions: Mean Convergence (4)

Elementary Differential Equations and Boundary Value Problems, 10th edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The WebAssign component includes a complete online version of the text and a variety of interactive study aids. All of these rich resources are linked together in a dynamic and interactive environment for students.

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## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Group Key
GO - GO Tutorial
XP - Extra Problem

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 1: Introduction
1.1 23 007 008 009 010 011 014 015 015.GO 016.GO 017 017.GO 018.GO 019 019.GO 020.GO 021 022 024 026 028 030 031 032
1.2 16 001 002 003 004 007 008 008.GO 009 010 011 012.GO 015 016 017 019 501.XP
1.3 25 001 001.GO 002 002.GO 003 003.GO 004 004.GO 005.GO 006 006.GO 009 015 016 017 018 018.GO 019 020 020.GO 021 022 023 024 025
Chapter 2: First Order Differential Equations
2.1 18 001 002 004 005 008 010 012 013 015 016.GO 018 020 023 028 031 032 039 042
2.2 15 001 004 005 008 009 013 016.GO 019 022 023 025 029 032 033 036
2.3 15 001 003 004 004.GO 005 007 009 012 020 023 024 024.GO 026 029 501.XP
2.4 14 001 002 004 005 007 009 010 011 014 018 021 028 030 032
2.5 7 003 004 008 009 012 017 023
2.6 16 001 003 006 008 010 010.GO 014 016 019 022 025 026 027 028 028.GO 031
2.7 15 001 002 004 005 006 008 009 010 011 012 012.GO 014 014.GO 017 018
2.8 10 001 002.GO 003 005 006 007 008 010 011 012
2.9 6 001 002 006.GO 007 010 015
Chapter 3: Second Order Linear Equations
3.1 15 001 002 006 007 009 010 012 015 016 017 021 023 025 026 027
3.2 21 001 004.GO 005 006 007 008.GO 009 012 018 020 022 024 025 028 029 031 034 035 036 042 047
3.3 17 001 003 004 006 008 009 010 011 014 018.GO 019 020.GO 023 036 039 041 045
3.4 19 002 003 004 008 011 012.GO 014 015 018 023 024.GO 025 027 030 034 035 040 042 044
3.5 19 001 002 003 005 007 008 010 011 014 015 016 016.GO 018 020 021 023 030 036 037
3.6 16 001 002 003 004 006 006.GO 007 010 013 015 017 024 025 029 030 031
3.7 15 001 003 004 006 008 010.GO 012 013 016 017 018 022 023 024 028
3.8 15 001 002 003 004 006 007 009 010 011 012 016 017 019 021 023
Chapter 4: Higher Order Linear Equations
4.1 17 001 003 004 005 006 007 008 009 010 011 014.GO 016 021 022 023 024 027
4.2 20 001 003 004 005 008.GO 010 011 012 014 015 018 019 022 024.GO 026 030 031 034 036 038
4.3 15 001 002 003 004 005 006 006.GO 008 009 010 011 012 014 016 018
4.4 12 001 002 003 004.GO 006 007 009 010 011 013 014 016
Chapter 5: Series Solutions of Second Order Linear Equations
5.1 17 001 002 003 004 005 007 008.GO 009 010 012 013 015 016 017 021 023 024
5.2 11 001 006 006.GO 008 011 014 015 017 023 024 027
5.3 16 001 002.GO 004 005 006 007 008 008.GO 011 013 015 016 018 019 020 024
5.4 23 001 003 004.GO 005 005.GO 008 009 012 012.GO 014 016 017 018 020 022 023 025 029 034 035 045 046 047
5.5 10 001 002.GO 003 005 007 008 009 010 011 015
5.6 12 001 002 003 005 006.GO 007 009 011 013 015 016 501.XP
5.7 4 001 002 003 005
Chapter 6: The Laplace Transform
6.1 17 001 004 005 006 007.GO 008.GO 010 012 013 016 017 018 020 021 022 025 027
6.2 18 001 002 003 005 006.GO 008 011 013 016.GO 017 019 021 022.GO 024 026 030 031 034
6.3 17 002 004 007 011 013 014 014.GO 017 019 022 022.GO 023 027 029 030 035 036
6.4 14 001 002 003 004.GO 006 008 009 011 012 014 016 017 019 021
6.5 11 001 002.GO 004 007 008 011 012 015 017 020 022
6.6 16 004 005 006 006.GO 008 009 010 010.GO 013 014 017 020 023 025 027 028
Chapter 7: Systems of First Order Linear Equations
7.1 13 001 002 004 005 007 008 009 010 010.GO 012 018 022 023
7.2 14 001 002 003 004 006 008 009 010 011 012.GO 014 016 017 021
7.3 15 001 002 003 005 007 008 011 013 014 016 019 020 023.GO 024 501.XP
7.4 3 006 006.GO 007
7.5 15 001 004.GO 005 007 009 011 013 015 017 018.GO 020 023 024 031 032
7.6 15 001 003 006.GO 007 008.GO 009 010 011 015 016 019 020 021 023 026
7.7 12 001 002 004 004.GO 006 007 008 009 010 011 012 017
7.8 9 001 003 006 007 009 012.GO 013 016 020
7.9 13 001 002 003 004 005 006 007 009 010 011 012 013 015
Chapter 8: Numerical Methods
8.1 14 001 002 004 004.GO 005 007 009 011 012 016 018 021 025 026
8.2 15 001 002 004 004.GO 005 006 007 008 010 012 016 018 020 023 025
8.3 11 001 002 003 004.GO 005 007 008 010 011 012 014
8.4 5 001 004.GO 005 009 011
8.5 4 001 004.GO 005 008
8.6 2 004 005
Chapter 9: Nonlinear Differential Equations and Stability
9.1 11 001 002.GO 004 006 007 010 011 012 013 014 015
9.2 12 001 004 005 006.GO 008 010 012 015 017 019 021 023
9.3 10 005 006 008.GO 010 012 014 016 018 019 024
9.4 10 001 003 004.GO 005 009 010 013 015 017 019
9.5 9 001 003 004.GO 005 007 009 010 011 501.XP
9.6 3 001 003 004.GO
9.7 7 001 003 004.GO 009 014 018 019
9.8 8 005 006 007 008 009 010 012 014
Chapter 10: Partial Differential Equations and Fourier Series
10.1 16 001 003 004 006 006.GO 007 008 009 012 014 016 017 018 020 021 022
10.2 17 001 002 004 005 007 009 011 014 016 016.GO 018 019 021 022 024 025 026
10.3 11 001 003 005 008 008.GO 010 012 013 014 015 016
10.4 17 001 003 004 005 006 008 009 012 016 018.GO 019 021 023 025 026 028 030
10.5 12 001 002 002.GO 004 005 007 009 011 013 014 017 019
10.6 13 001 002.GO 003 005 007 008 010 011 013 016 017 019 022
10.7 10 001 002 003 005 007 010 011 014 015 024
10.8 11 001 002 003 006 007 008 011 012 013 014 016
Chapter 11: Boundary Value Problems and Sturm-Liouville Theory
11.1 15 001 002 003 004 005 007 008 008.GO 010 012 014 017 019 020 021
11.2 18 001 002 002.GO 004 006 007 008 009 011 012 013 014 015 016 018 025 026 028
11.3 18 001 003 004 004.GO 006 008 010 011 013 017 019 020 021 024 025 031 032 034
11.4 1 001
11.5 2 003 010
11.6 4 002 003 007 008
Total 962