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High Quality Content by WIKIPEDIA articles! In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of its derivatives with respect to that variable. A simple example is Newton's second law of motion, which leads to the differential equation m frac{d^2 x(t)}{dt^2} = F(x(t)),, for the motion of a particle of constant mass m. In general, the force F depends upon the position of the particle x(t) 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)).