  We develop a partial Hamiltonian framework to obtain reductions and
closed-form solutions via first integrals of current value Hamiltonian systems
of ordinary differential equations (ODEs).
  The approach is algorithmic and applies to many state and costate variables
of the current value Hamiltonian. However, we apply the method to models with
one control, one state and one costate variable to illustrate its
effectiveness. The current value Hamiltonian systems arise in economic growth
theory and other economic models. We explain our approach with the help of a
simple illustrative example and then apply it to two widely used economic
growth models: the Ramsey model with a constant relative risk aversion (CRRA)
utility function and Cobb Douglas technology and a one-sector AK model of
endogenous growth are considered. We show that our newly developed systematic
approach can be used to deduce results given in the literature and also to find
new solutions.
