The solution of a DAE consists of two parts, first the search for consistent initial values and second the computation of a trajectory. To find consistent initial values it is often necessary to consider the derivatives of some of the component functions of the DAE. The highest order of a derivative that is necessary for this process is called the "differentiation index". The equations derived in computing the index and consistent initial values may also be of use in the computation of the trajectory. A semi-explicit DAE system can be converted to an implicit one by decreasing the differentiation index by one, and vice versa.