IPOPT and APOPT are two of the large-scale NLP solvers are available in the APM Optimization Toolbox. Models are posed in differential or algebraic equation form. Differential variables can be included on the right or left side of the equation because the modeling language allows open-equation format.
Higher index DAEs can also be solved. One example of an index-3 DAE is a pendulum example available for download here:
Below is a list of features of the optimization toolbox:
-Exact first and second derivatives in sparse form
-Exact sparsity detection
-Loss-less model reduction
-Created from C++ / F90 source code
-Differential and algebraic equations in open format
-Equality or inequality equations (e.g. expr1 <= expr2 < expr3)
-IDE for model development with syntax highlighting
-Interfaces to a number of commercial and open-source solvers
-A number of users describe it as "Intuitively useable"
Additional documentation and reviews are available from the wiki website.