  The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general
potential $\rm V(\phi)$ in the scalar field inflation scenario. The Bohmian
approach (a WKB-like formalism) was employed in order to constraint a generic
form of potential to the most suited to drive inflation, from here a family of
potentials emerges; in particular we select an exponential potential as the
first non trivial case and remains the object of interest of this work. The
solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected
potential in this scheme. Using Hamilton's approach and equations of motion for
a scalar field $\rm \phi$ with standard kinetic energy, we find the exact
solutions to the complete set of Einstein-Klein-Gordon (EKG) equations without
the need of the slow-roll approximation (SR). In order to contrast this model
with observational data (Planck 2018 results), the inflationary observables:
the tensor-to-scalar ratio and the scalar spectral index are derived in our
proper time, and then evaluated under the proper condition such as the number
of e-folding corresponds exactly at 50-60 before inflation ends. The employed
method exhibits a remarkable simplicity with rather interesting applications in
the near future.
