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# Ordinary dtions of only ## Ordinary dtions of only

In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable.
A simple example is Newton's second law of motion, which leads to the differential equation

for the motion of a particle of constant mass m. In general, the force F depends upon the position x(t) of the particle at time t, and thus the unknown function x(t) appears on both sides of the differential equation, as is indicated in the notation F(x(t)).
Ordinary differential equations are distinguished from partial differential equations, which involve partial derivatives of functions of several variables.
Ordinary differential equations arise in many different contexts including geometry, mechanics, astronomy and population modelling. Many mathematicians have studied differential equations and c

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