Ordinary differential equation

An ordinary differential equation (often shortened to ODE) is a differential equation which contains one free variable, and its derivatives. Ordinary differential equations are used for many scientific models and predictions. The term "ordinary" is used to differentiate them from partial differential equations, which contain more than one free variable, and their derivatives.
Numerical methods.
Since ODEs have appeared in mathematics and physics, many scientists have studied methods to solve them. But unfortunately, no one could establish methods to solve any kind of ODE. Therefore, numerical methods for ODEs are widely studied since the appearance of computers.