[en] The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $V(\mathrm{\varphi <!--\; ??\; -->})$ 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 $\mathrm{\varphi <!--\; ??\; -->}$ 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 (Akrami et al. 2018, arXiv:1807.06211 , (Planck Collaboration) 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.