Ordinary Differential Equations Chapter 3.5 Solutions

On this webpage you will find my solutions to the tenth edition of "Elementary Differential Equations and Boundary Value Problems" by Boyce and DiPrima. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.

• 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

Section 7.5		Section 7.6		Section 7.7	Section 7.8	Section 7.9
Problem 1	Problem 26	Problem 1 | Solution	Problem 26 | Solution	Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution
Problem 2	Problem 27	Problem 2 | Solution	Problem 27 | Solution	Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution
Problem 3	Problem 28 | Solution	Problem 3 | Solution	Problem 28 | Solution	Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution
Problem 4	Problem 29 | Solution	Problem 4 | Solution	Problem 29 | Solution	Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution
Problem 5	Problem 30 | Solution	Problem 5 | Solution	Problem 30 | Solution	Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution
Problem 6	Problem 31 | Solution	Problem 6 | Solution	Problem 31 | Solution	Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution
Problem 7	Problem 32 | Solution	Problem 7 | Solution		Problem 7 | Solution	Problem 7 | Solution	Problem 7 | Solution
Problem 8	Problem 33 | Solution	Problem 8 | Solution		Problem 8 | Solution	Problem 8 | Solution	Problem 8 | Solution
Problem 9		Problem 9 | Solution		Problem 9 | Solution	Problem 9 | Solution	Problem 9 | Solution
Problem 10		Problem 10 | Solution		Problem 10 | Solution	Problem 10 | Solution	Problem 10 | Solution
Problem 11		Problem 11 | Solution		Problem 11 | Solution	Problem 11 | Solution	Problem 11 | Solution
Problem 12		Problem 12 | Solution		Problem 12 | Solution	Problem 12 | Solution	Problem 12 | Solution
Problem 13		Problem 13 | Solution		Problem 13 | Solution	Problem 13 | Solution	Problem 13 | Solution
Problem 14		Problem 14 | Solution		Problem 14 | Solution	Problem 14 | Solution	Problem 14 | Solution
Problem 15		Problem 15 | Solution		Problem 15 | Solution	Problem 15 | Solution	Problem 15 | Solution
Problem 16		Problem 16 | Solution		Problem 16 | Solution	Problem 16 | Solution	Problem 16 | Solution
Problem 17		Problem 17 | Solution		Problem 17 | Solution	Problem 17 | Solution	Problem 17 | Solution
Problem 18		Problem 18 | Solution		Problem 18 | Solution	Problem 18 | Solution	Problem 18 | Solution
Problem 19		Problem 19 | Solution			Problem 19 | Solution
Problem 20		Problem 20 | Solution			Problem 20 | Solution
Problem 21		Problem 21 | Solution			Problem 21 | Solution
Problem 22		Problem 22 | Solution			Problem 22 | Solution
Problem 23		Problem 23 | Solution
Problem 24		Problem 24 | Solution
Problem 25		Problem 25 | Solution

Section 8.1		Section 8.2
Problem 1 | Solution	Problem 26 | Solution	Problem 1 | Solution	Problem 26 | Solution
Problem 2 | Solution	Problem 27 | Solution	Problem 2 | Solution	Problem 27 | Solution
Problem 3 | Solution		Problem 3 | Solution
Problem 4 | Solution		Problem 4 | Solution
Problem 5 | Solution		Problem 5 | Solution
Problem 6 | Solution		Problem 6 | Solution
Problem 7 | Solution		Problem 7 | Solution
Problem 8 | Solution		Problem 8 | Solution
Problem 9 | Solution		Problem 9 | Solution
Problem 10 | Solution		Problem 10 | Solution
Problem 11 | Solution		Problem 11 | Solution
Problem 12 | Solution		Problem 12 | Solution
Problem 13 | Solution		Problem 13 | Solution
Problem 14 | Solution		Problem 14 | Solution
Problem 15 | Solution		Problem 15 | Solution
Problem 16 | Solution		Problem 16 | Solution
Problem 17 | Solution		Problem 17 | Solution
Problem 18 | Solution		Problem 18 | Solution
Problem 19 | Solution		Problem 19 | Solution
Problem 20 | Solution		Problem 20 | Solution
Problem 21 | Solution		Problem 21 | Solution
Problem 22 | Solution		Problem 22 | Solution
Problem 23 | Solution		Problem 23 | Solution
Problem 24 | Solution		Problem 24 | Solution
Problem 25 | Solution		Problem 25 | Solution

Section 8.3	Section 8.4	Section 8.5	Section 8.6
Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution
Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution
Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution
Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution
Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution
Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution
Problem 7 | Solution	Problem 7 | Solution	Problem 7 | Solution
Problem 8 | Solution	Problem 8 | Solution	Problem 8 | Solution
Problem 9 | Solution	Problem 9 | Solution	Problem 9 | Solution
Problem 10 | Solution	Problem 10 | Solution
Problem 11 | Solution	Problem 11 | Solution
Problem 12 | Solution	Problem 12 | Solution
Problem 13 | Solution	Problem 13 | Solution
Problem 14 | Solution	Problem 14 | Solution
Problem 15 | Solution	Problem 15 | Solution
	Problem 16 | Solution

Section 9.1	Section 9.2		Section 9.3
Problem 1 | Solution	Problem 1 | Solution	Problem 26 | Solution	Problem 1 | Solution	Problem 26 | Solution
Problem 2 | Solution	Problem 2 | Solution	Problem 27 | Solution	Problem 2 | Solution	Problem 27 | Solution
Problem 3 | Solution	Problem 3 | Solution	Problem 28 | Solution	Problem 3 | Solution	Problem 28 | Solution
Problem 4 | Solution	Problem 4 | Solution		Problem 4 | Solution	Problem 29 | Solution
Problem 5 | Solution	Problem 5 | Solution		Problem 5 | Solution	Problem 30 | Solution
Problem 6 | Solution	Problem 6 | Solution		Problem 6 | Solution
Problem 7 | Solution	Problem 7 | Solution		Problem 7 | Solution
Problem 8 | Solution	Problem 8 | Solution		Problem 8 | Solution
Problem 9 | Solution	Problem 9 | Solution		Problem 9 | Solution
Problem 10 | Solution	Problem 10 | Solution		Problem 10 | Solution
Problem 11 | Solution	Problem 11 | Solution		Problem 11 | Solution
Problem 12 | Solution	Problem 12 | Solution		Problem 12 | Solution
Problem 13 | Solution	Problem 13 | Solution		Problem 13 | Solution
Problem 14 | Solution	Problem 14 | Solution		Problem 14 | Solution
Problem 15 | Solution	Problem 15 | Solution		Problem 15 | Solution
Problem 16 | Solution	Problem 16 | Solution		Problem 16 | Solution
Problem 17 | Solution	Problem 17 | Solution		Problem 17 | Solution
Problem 18 | Solution	Problem 18 | Solution		Problem 18 | Solution
Problem 19 | Solution	Problem 19 | Solution		Problem 19 | Solution
Problem 20 | Solution	Problem 20 | Solution		Problem 20 | Solution
Problem 21 | Solution	Problem 21 | Solution		Problem 21 | Solution
Problem 22 | Solution	Problem 22 | Solution		Problem 22 | Solution
	Problem 23 | Solution		Problem 23 | Solution
	Problem 24 | Solution		Problem 24 | Solution
	Problem 25 | Solution		Problem 25 | Solution

Section 9.4	Section 9.5	Section 9.6	Section 9.7	Section 9.8
Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution	Problem 1 | Solution
Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution	Problem 2 | Solution
Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution	Problem 3 | Solution
Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution	Problem 4 | Solution
Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution	Problem 5 | Solution
Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution	Problem 6 | Solution
Problem 7 | Solution	Problem 7 | Solution	Problem 7 | Solution	Problem 7 | Solution	Problem 7 | Solution
Problem 8 | Solution	Problem 8 | Solution	Problem 8 | Solution	Problem 8 | Solution	Problem 8 | Solution
Problem 9 | Solution	Problem 9 | Solution	Problem 9 | Solution	Problem 9 | Solution	Problem 9 | Solution
Problem 10 | Solution	Problem 10 | Solution	Problem 10 | Solution	Problem 10 | Solution	Problem 10 | Solution
Problem 11 | Solution	Problem 11 | Solution	Problem 11 | Solution	Problem 11 | Solution	Problem 11 | Solution
Problem 12 | Solution	Problem 12 | Solution	Problem 12 | Solution	Problem 12 | Solution	Problem 12 | Solution
Problem 13 | Solution	Problem 13 | Solution		Problem 13 | Solution	Problem 13 | Solution
Problem 14 | Solution	Problem 14 | Solution		Problem 14 | Solution	Problem 14 | Solution
Problem 15 | Solution	Problem 15 | Solution		Problem 15 | Solution	Problem 15 | Solution
Problem 16 | Solution	Problem 16 | Solution		Problem 16 | Solution
Problem 17 | Solution			Problem 17 | Solution
Problem 18 | Solution			Problem 18 | Solution
Problem 19 | Solution			Problem 19 | Solution
			Problem 20 | Solution
			Problem 21 | Solution

Ordinary Differential Equations Chapter 3.5 Solutions

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