Ordinary differential equation
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
