Intro
Preface
Contents
Chapter 1: Introduction
Chapter 2: First-Order Differential Equations
2.1 Existence and Uniqueness of a Solution
2.2 Integral Curves and Isoclines
2.3 Separable Equations
2.4 Linear First-Order Differential Equations
2.4.1 Homogeneous Linear Equations
2.4.2 Nonhomogeneous Linear Equations: Method of a Parameter Variation
2.4.3 Nonhomogeneous Linear Equations: Method of Integrating Factor
2.4.4 Nonlinear Equations That Can Be Transformed into Linear Equations
2.5 Exact Equations

2.6 Equations Unresolved with Respect to a Derivative
2.6.1 Regular and Irregular Solutions
2.6.2 Lagrangeś Equation
2.6.3 Clairautś Equation
2.7 Qualitative Approach for Autonomous First-Order Equations: Equilibrium Solutions and Phase Lines
2.8 Examples of Problems Leading to First-Order Differential Equations
Chapter 3: Differential Equations of Order n > 1
3.1 General Considerations
3.2 Second-Order Differential Equations
3.3 Reduction of Order
3.4 Linear Second-Order Differential Equations
3.4.1 Homogeneous Equations

3.4.2 Reduction of Order for a Linear Homogeneous Equation
3.4.3 Nonhomogeneous Equations
3.5 Linear Second-Order Equations with Constant Coefficients
3.5.1 Homogeneous Equations
3.5.2 Nonhomogeneous Equations: Method of Undetermined Coefficients
3.6 Linear Second-Order Equations with Periodic Coefficients
3.6.1 Hill Equation
3.6.2 Mathieu Equation
3.7 Linear Equations of Order n > 2
3.8 Linear Equations of Order n > 2 with Constant Coefficients
3.9 Euler Equation
3.10 Applications
3.10.1 Mechanical Oscillations
3.10.2 RLC Circuit

3.10.3 Floating Body Oscillations
Chapter 4: Systems of Differential Equations
4.1 General Considerations
4.2 Systems of First-Order Differential Equations
4.3 Systems of First-Order Linear Differential Equations
4.4 Systems of Linear Homogeneous Differential Equations with Constant Coefficients
4.5 Systems of Linear Nonhomogeneous Differential Equations with Constant Coefficients
4.6 Matrix Approach
4.6.1 Homogeneous Systems of Equations
4.6.1.1 Matrix Equation
4.6.1.2 Series Solution for a Constant Matrix A
4.6.1.3 The Case of a Diagonalizable Constant Matrix A

4.6.1.4 The Case of a Non-diagonalizable Constant Matrix A
4.6.2 Nonhomogeneous Systems of Equations
4.6.2.1 The General Case
4.6.2.2 The Case of a Constant Matrix A
4.7 Applications
4.7.1 Charged Particle in a Magnetic Field
4.7.2 Precession of a Magnetic Moment in a Magnetic Field
4.7.3 Spring-Mass System
4.7.4 Mutual Inductance
Chapter 5: Qualitative Methods and Stability of ODE Solutions
5.1 Phase Plane Approach
5.2 Phase Portraits and Stability of Solutions in the Case of Linear Autonomous Systems
5.2.1 Equilibrium Points