  We discuss the calculation of the derivatives of ODE systems with the
automatic differentiation tool ADiMat. Using the well-known Lotka-Volterra
equations and the ode23 ODE solver as examples we show the analytic derivatives
and detail how to differentiate a top-level function that calls ode23 somewhere
with ADiMat. This involves the manual construction of substitution function to
propagate the derivatives in forward and reverse mode. We also show how to use
the reverse mode code to evaluate the Hessian in forward-over-reverse mode.
