Differential algebraic equations (DAEs) define a differential equation
on a manifold. A number of ways have been developed to numerically solve
some classes of DAEs. Motivated by problems in control theory, numerical
simulation, and the use of general purpose modeling environments, recent
research has considered the embedding of the DAE solutions of a general DAE
into the solutions of an ODE where the added dynamics have special properties.
This paper both provides new results on the linear time varying case and
considers the important nonlinear case.