The curve is usually called a trajectory or an orbit. The (vector) differential equation is reformulated as a geometrical description of the curve, that is, as a differential equation in terms of the phase space variables only, without the original time parametrization.
The curve is commonly known as a trajectory or an orbit. The (vector) differential equation is reformulated into a geometrical description of the curve, which involves expressing it in terms of phase space variables exclusively and ignoring the initial time parameterization.