It is a non-trivial task to convert arbitrary DAE systems into ODEs for solution by pure ODE solvers. Techniques which can be employed include "Pantelides algorithm" and "dummy derivative index reduction method". Alternatively, a direct solution of high-index DAEs with inconsistent initial conditions is also possible. This solution approach involves a transformation of the derivative elements through "orthogonal collocation on finite elements" or "direct transcription" into algebraic expressions. This allows DAEs of any index to be solved without rearrangement in the open equation form