An ordinary differential equation or ODE is an equation containing a function of one independent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

http://en.wikipedia.org/wiki/Ordinary_differential_equation

Linear differential equations are well-defined and understood, and usually have exact closed-form solutions. By contrast, ODEs that lack additive solutions are nonlinear. For those we can use graphical and numerical methods, the latter sometimes by hand, but possibly by computer.

We use ODEs to solve Simple Harmonic Motion, such as a weight suspended on a spring, or a pendulum swinging through a very small angle.

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