 In matrix form

For a system of the form formula_10, some sources also require that the Jacobian matrix formula_11 be non-singular in order to call this an implicit ODE [system]; an implicit ODE system satisfying this Jacobian non-singularity condition can be transformed into an explicit ODE system.In the same sources, implicit ODE systems with a singular Jacobian are termed differential algebraic equations (DAEs).This distinction is not merely one of terminology; DAEs have fundamentally different characteristics and are generally more involved to solve than (nonsingular) ODE systems.