Differential equations with boundary value problems 2nd edition solutions

Problems 1.1.1 - 1.3.16

Problems 1.3.17 - 2.2.14

Problems 2.2.15 - 2.4.14

Problems 2.4.15 - 2.6.20

Problems 2.6.21 - 2.9.12

Problems 2.9.13 - 3.1.8

Problems 3.1.9 - 3.2.48

Problems 3.2.49 - 3.4.18

Problems 3.4.19 - 3.5.39

Problems 3.6.1 - 3.8.4

Problems 3.8.5 - 4.2.22

Problems 4.2.23 - 5.1.12

Problems 5.1.13 - 5.3.24

Problems 5.3.25 - 5.5.12

Problems 5.5.13 - 6.1.28

Problems 6.1.29 - 6.3.28

Problems 6.3.29 - 6.6.4

Problems 6.6.5 - 7.2.20

Problems 7.2.21 - 7.5.16

Problems 7.5.17 - 7.8.4

Problems 7.8.5 - 8.1.27

Problems 8.2.1 - 8.5.9

Problems 8.6.1 - 9.3.8

Problems 9.3.9 - 9.6.8

Problems 9.6.9 - 10.2.4

Problems 10.2.5 - 10.4.24

Problems 10.4.25 - 10.7.4

Problems 10.7.5 - 11.2.8

Problems 11.2.9 - 11.6.13

• Chapter 1: Introduction
  • Section 1.1: Some Basic Mathematical Models; Direction Fields
  • Section 1.2: Solutions of Some Differential Equations
  • Section 1.3: Classification of Differential Equations
  • Section 1.4: Historical Remarks
  
  
• Chapter 2: First Order Differential Equations
  • Section 2.1: Linear Equations; Method of Integrating Factors
  • Section 2.2: Separable Equations
  • Section 2.3: Modeling with First Order Equations
  • Section 2.4: Differences Between Linear and Nonlinear Equations
  • Section 2.5: Autonomous Equations and Population Dynamics
  • Section 2.6: Exact Equations and Integrating Factors
  • Section 2.7: Numerical Approximations: Euler's Method
  • Section 2.8: The Existence and Uniqueness Theorem
  • Section 2.9: First Order Difference Equations
  
  
• Chapter 3: Second Order Linear Equations
  • Section 3.1: Homogeneous Equations with Constant Coefficients
  • Section 3.2: Solutions of Linear Homogeneous Equations; the Wronskian
  • Section 3.3: Complex Roots of the Characteristic Equation
  • Section 3.4: Repeated Roots; Reduction of Order
  • Section 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients
  • Section 3.6: Variation of Parameters
  • Section 3.7: Mechanical and Electrical Vibrations
  • Section 3.8: Forced Vibrations
  
  
• Chapter 4: Higher Order Linear Equations
  • Section 4.1: General Theory of nth Order Linear Equations
  • Section 4.2: Homogeneous Equations with Constant Coefficients
  • Section 4.3: The Method of Undetermined Coefficients
  • Section 4.4: The Method of Variation of Parameters

• Chapter 5: Series Solutions of Second Order Linear Equations
  • Section 5.1: Review of Power Series
  • Section 5.2: Series Solutions Near an Ordinary Point, Part I
  • Section 5.3: Series Solutions Near an Ordinary Point, Part II
  • Section 5.4: Euler Equations; Regular Singular Points
  • Section 5.5: Series Solutions Near a Regular Singular Point, Part I
  • Section 5.6: Series Solutions Near a Regular Singular Point, Part II
  • Section 5.7: Bessel's Equation
  
  
• Chapter 6: The Laplace Transform
  • Section 6.1: Definition of the Laplace Transform
  • Section 6.2: Solution of Initial Value Problems
  • Section 6.3: Step Functions
  • Section 6.4: Differential Equations with Discontinuous Forcing Functions
  • Section 6.5: Impulse Functions
  • Section 6.6: The Convolution Integral
  
  
• Chapter 7: Systems of First Order Linear Equations
  • Section 7.1: Introduction
  • Section 7.2: Review of Matrices
  • Section 7.3: Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
  • Section 7.4: Basic Theory of Systems of First Order Linear Equations
  • Section 7.5: Homogeneous Linear Systems with Constant Coefficients
  • Section 7.6: Complex Eigenvalues
  • Section 7.7: Fundamental Matrices
  • Section 7.8: Repeated Eigenvalues
  • Section 7.9: Nonhomogeneous Linear Systems
  
  
• Chapter 8: Numerical Methods
  • Section 8.1: The Euler or Tangent Line Method
  • Section 8.2: Improvements on the Euler Method
  • Section 8.3: The Runge-Kutta Method
  • Section 8.4: Multistep Methods
  • Section 8.5: Systems of First Order Equations
  • Section 8.6: More on Errors; Stability
  
  

• Chapter 9: Nonlinear Differential Equations and Stability
  • Section 9.1: The Phase Plane: Linear Systems
  • Section 9.2: Autonomous Systems and Stability
  • Section 9.3: Locally Linear Systems
  • Section 9.4: Competing Species
  • Section 9.5: Predator-Prey Equations
  • Section 9.6: Liapunov's Second Method
  • Section 9.7: Periodic Solutions and Limit Cycles
  • Section 9.8: Chaos and Strange Attractors: The Lorenz Equations
  
  
• Chapter 10: Partial Differential Equations and Fourier Series
  • Section 10.1: Two-Point Boundary Value Problems
  • Section 10.2: Fourier Series
  • Section 10.3: The Fourier Convergence Theorem
  • Section 10.4: Even and Odd Functions
  • Section 10.5: Separation of Variables; Heat Conduction in a Rod
  • Section 10.6: Other Heat Conduction Problems
  • Section 10.7: The Wave Equation: Vibrations of an Elastic String
  • Section 10.8: Laplace's Equation
  
  
• Chapter 11: Boundary Value Problems and Sturm-Liouville Theory
  • Section 11.1: The Occurence of Two-Point Boundary Value Problems
  • Section 11.2: Sturm-Liouville Boundary Value Problems
  • Section 11.3: Nonhomogeneous Boundary Value Problems
  • Section 11.4: Singular Sturm-Liouville Problems
  • Section 11.5: Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
  • Section 11.6: Series of Orthogonal Functions: Mean Convergence