They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the derivatives of all components of the function "x" because these may not all appear (i.e. some equations are algebraic); technically the distinction between an implicit ODE system may be rendered explicit and a DAE system is that the Jacobian matrix formula_5 is a singular matrix for a DAE system. This distinction between ODEs and DAEs is made because DAEs have different characteristics and are generally more difficult to solve.