Ordinary differential equation

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]

^ 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.
^ "What is the origin of the term "ordinary differential equations"?". hsm.stackexchange.com. Stack Exchange. Retrieved 2016-07-28.
^ Karras, Tero; Aittala, Miika; Aila, Timo; Laine, Samuli (2022). "Elucidating the Design Space of Diffusion-Based Generative Models". Arxiv preprint. doi:10.48550/arXiv.2206.00364.

[Zill2012-1] 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 preprint. doi:10.48550/arXiv.2206.00364.

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