adj. 1. (of a system of ordinary differential equations) not explicitly depending on the variable of differentiation (often time); that is, such that there is no explicit occurrence of the independent variable in the equation dy/dt = f(y). For example, the equation dx/dt = x is autonomous, but the equation dx/dt = t is not. 2. (of an ordinary differential equation of the second-order) able to be reduced to a first-order equation by writing and regarding u as the independent variable, where u is the dependent variable, and t the independent variable of the given equation.