# 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 | edit source]

## Existence of ODEs[edit | edit source]

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

## First order equations[edit | edit source]

- One-dimensional first-order linear equations
- Separable equations
- Integrating factor
- Exact equations
- Linearize
- Autonomous equations
- 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 | edit source]

- Homogeneous second order equations
- Nonhomogeneous second order equations:Method of undetermined coefficients
- Nonhomogeneous second order equations: Variations of parameters
- Nonhomogeneous second order equations: Reduction of order

## Higher order equations[edit | edit source]

- Homogeneous higher order equations
- Nonhomogeneous higher order equations
- Linear autonomous equations of higher order with constant coefficients
- Linear autonomous equations of higher order with varying coefficients

## Systems of equations[edit | edit source]

- Homogeneous linear systems with constant coefficients
- Nonhomogeneous linear systems: Diagonalization method
- Nonhomogeneous linear systems: Method of undetermined coefficients
- Nonhomogeneous linear systems: Integrating factor
- Nonhomogeneous linear systems: Variation of parameters

## Laplace Transform[edit | edit source]

## Nonlinear systems of equations[edit | edit source]

## Lyapunov's stability results[edit | edit source]

## Sources[edit | edit source]

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.