ode15s and differential algebraic equations (DAE) of index 3

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According to the post below, ode15s and ode23t require the DAE to be of index 1. I think that for constrained mechanical systems, the DAEs are typically of index 3. Does MATLAB have a means of solving these equations?
Previous post: What is the meaning of "This DAE appears to be of index greater than 1" using ODE solvers for solving Differential Algebraic Equations (DAE) in MATLAB 7.4 (R2007a)?

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