Ordinary differential equation

parabolic projectile motion showing velocity vector
The trajectory of a projectile launched from a cannon follows a curve determined by an ordinary differential equation that is derived from Newton's second law.
Differential equations
Scope
Fields
Applied mathematics
Social sciences
List of named differential equations
Classification
Types
By variable type
Features
Relation to processes
Solution
Existence and uniqueness
General topics
Solution methods
People
List

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions.[1] The term "ordinary" is used in contrast with partial differential equations (PDEs) which may be with respect to more than one independent variable,[2] and, less commonly, in contrast with stochastic differential equations (SDEs) where the progression is random.[3]

  1. ^ Dennis G. Zill (15 March 2012). A First Course in Differential Equations with Modeling Applications. Cengage Learning. ISBN 978-1-285-40110-2. Archived from the original on 17 January 2020. Retrieved 11 July 2019.
  2. ^ "What is the origin of the term "ordinary differential equations"?". hsm.stackexchange.com. Stack Exchange. Retrieved 2016-07-28.
  3. ^ Karras, Tero; Aittala, Miika; Aila, Timo; Laine, Samuli (2022). "Elucidating the Design Space of Diffusion-Based Generative Models". arXiv:2206.00364 [cs.CV].