# Differential Equations

!!! Laplace Table !!!

!!! Midterm Exam !!! 2019 Summer Midterm !!!

 Chapter Subchapter Exercises 1. Introduction Classification of Differential Equations 2. First Order Differential Equations 2. Solved Problems Linear Equations Linear_Ex Seperable Equations Seperable_Ex Exact Equations Exact_Ex Bernoulli Equations Bernoulli_Ex Homogeneous Equations Homogeneous_Ex 3. Second Order Differential Equations 3.1  Homogeneous Equations with Constant Coefficients 1-18 ;  Answers 3.2  Solutions of Linear Homogeneous Equations; the Wronskian 1-6, 17-20 ;  Answers 3.3  Complex Roots of the Characteristic Equation 7-22 ;  Answers 3.4  Repeated Roots; Reduction of Order 1-14, 23-30 ;  Answers 3.5  Nonhomogeneous Equations; Method of Undetermined Coefficients 1-20 ;  Answers 3.6  Variation of Parameters 1-17 ;  Answers 4. Higher Order Differential Equations 4.1  General Theory of nth Order Linear Equations 7-17 ;  Answers 4.2  Homogeneous Equations with Constant Coefficients 11-24 ;  Answers 4.3  The Method of Undetermined Coefficients 1-18 ;  Answers 4.4  The Method of Variation of Parameters 6. The Laplace Transform 6.1  Definition of the Laplace Transform 6.1 6.2  Solution of Initial Value Problems 1-23 ;  Answers 6.3  Step Functions 6.4  Diffrential Equations with Discontinuous Forcing Functions

Resources:

Elementary Differential Equations, 10th Edition – William E. Boyce

Paul’s Online Math Notes

Schaum’s Outline of Differential Equations, Richard Bronson & Gabriel Costa