VNODE-LP is a C++ package with which you should be able to achieve the desired task:

> VNODE-LP is a C++ package for computing bounds on solutions in IVPs for ODEs. In contrast to traditional ODE solvers, which compute approximate solutions, this solver tries to prove that a unique solution to a problem exists and then computes bounds that contain this solution. Such bounds can be used to help prove a theoretical result, check if a solution satisfies a condition in a safety-critical calculation, or simply to verify the results produced by a traditional ODE solver.

This package is a successor of the VNODE package of N. Nedialkov (mentioned above in the comments).

It is free and can be downloaded here:<br>
http://www.cas.mcmaster.ca/~nedialk/vnodelp/