# Ordinary Differential Equations

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**Ordinary Differential Equations**

covering uses of and solutions to ordinary differential equations

This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. It is hoped that this book will provide information about the whole area of differential equations, but for the moment it will concentrate on the simpler equations.

## Table of contents[edit]

- Introduction
- Form and Solutions of Differential Equations
- First-Order Differential Equations
- Separation of Variables
- Linear Differential Equations
- Exact Differential Equations
- Substitution Methods
- Bernoulli Equations
- Ricatti Equations
- Orthogonal and Oblique Trajectories
- Equations of higher degrees
- Equations without x or y
- Equations that are homogeneous in x and y
- d'Alembert's Equation
- Clairaut Equations
- Legendre Transformations
- Graphing Differential Equations

- Second-Order Differential Equations
- Higher Order Differential Equations
- Linear equations
- Integration methods

- Sturm-Liouville theory
- Systems of linear differential equations
- Nonlinear Systems
- Green's Functions
- Existence and Uniqueness of Solutions
- Continuous Transformation Groups
- Glossary
- List of Some Equations
- Help Needed
- Roadmap

## Sources[edit]

Differential Equations and Boundary Value Problems- C.H. Edwards Jr and David E. Penny

MIT Open Courseware- http://ocw.mit.edu/index.html