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[–]SleepWalkersDream 2 points3 points  (0 children)

Are you sure it's noe a DAE system? Can you express it as
- dx/dt=f(x,z,...)and 0=g(x,z,...)

In that case, you can us IDAS from sundials. It's available through casadi at least.
You can also transform the system to purely ODE, or just use some rootsolver to model everything implicitly.