Difference between revisions of "Ordinary differential equation"
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In [[mathematics]], an '''ordinary differential equation''' (or '''ODE''') is a [[differential equation]] containing a function or functions of one [[Dependent and independent variables|independent variable]] and its derivatives. | In [[mathematics]], an '''ordinary differential equation''' (or '''ODE''') is a [[differential equation]] containing a function or functions of one [[Dependent and independent variables|independent variable]] and its derivatives. | ||
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| + | == Description == | ||
The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. | The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. | ||
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* [[Dependent and independent variables]] | * [[Dependent and independent variables]] | ||
* [[Differential equation]] | * [[Differential equation]] | ||
| + | * [[Euler method]] | ||
== External links == | == External links == | ||
* [https://en.wikipedia.org/wiki/Ordinary_differential_equation Ordinary differential equation] @ Wikipedia | * [https://en.wikipedia.org/wiki/Ordinary_differential_equation Ordinary differential equation] @ Wikipedia | ||
Revision as of 09:24, 5 February 2016
In mathematics, an ordinary differential equation (or ODE) is a differential equation containing a function or functions of one independent variable and its derivatives.
Description
The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
Linear differential equations, which have solutions that can be added and multiplied by coefficients, are well-defined and understood, and exact closed-form solutions are obtained.
By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form. Instead, exact and analytic solutions of ODEs are in series or integral form.
Graphical and numerical methods, applied by hand or by computer, may approximate solutions of ODEs and perhaps yield useful information, often sufficing in the absence of exact, analytic solutions.
See also
External links
- Ordinary differential equation @ Wikipedia
