# Ordinary Differential Equations

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Ordinary differential equations are equations involving derivatives in one direction, to be solved for a solution curve.

## Table of contents[edit]

## First order equations[edit]

- One-dimensional first-order linear equations
- Separable equations: Separation of variables
- Derived cases 1: Rational functions in the right hand side
- Derived cases 2: Bernoulli equations, Ricatti equations
- Derived cases 3: Euler factors

## Second order equations[edit]

## Higher order equations[edit]

## 2D systems of equations[edit]

- Linear autonomous equations of higher order with constant coefficients
- Two-dimensional exact differential equations
- Linear autonomous equations of higher order with varying coefficients

## = Theory of general explicit ODEs[edit]

- Preliminaries from calculus
- The Picard–Lindelöf theorem
- Peano's theorem
- Blow-ups and moving to boundary
- Dependence on parameters

## Linear ODEs (higher order and multidimensional)[edit]

- Multidimensional linear equations with constant coefficients
- Homogenous linear equations with varying coefficients
- General linear equations

## 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

- Kong, Qingkai (0000).
*A Short Course in Ordinary Differential Equations*. Universe: Publisher. - Walter, Wolfgang (1998).
*Ordinary Differential Equations*. New York: Springer.