  Time-independent non-linear Schr\"{o}dinger-type (NLS) formulation of FRW
cosmology with canonical scalar field are considered in case of two barotropic
fluids. We derived Friedmann formulation variables in terms of NLS variables.
Seven exact solutions found by D'Ambroise \cite{DAmbroise:2010dgl} and one new
found solution are explored and tested in cosmology. The result suggests that
time-independent NLS formulation of cosmology case should be upgraded to the
time-dependent case.
