We have shown that generalizing slightly the notion of solution transforms somesingular problems into regular ones. Moreover any ODE and DAE code can be adapted to this formulation and so one can use standard software to treat some problems that were previously considered as requiring special attention. The analysis presented of the singularities of general higher index problems is probably not easier than fully nonlinear case, where one might expect that the jet space techniques could be helpful, set for definition of jet spaces.
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