Various approaches to the theology of polymer solutions and melts have resulted in an overabundance of constitutive equations (CEs). None of these equations can describe the entire set of available theological data in a consistent fashion, even for simple flows. Additionally, almost all the CEs suggested in the literature have recently been determined to be unstable in either the Hadamard or dissipative sense without any physical reason. In this paper, we attempt to describe simple flow data for LDPE Melt I/IUPAC A/IUPAC X, HDPE II, PS I, PIB P-20 and PIB L80 with a certain class of differential CEs, while complying with the global isothermal stability constraints. For simplicity, only one or two nonlinear parameters additional to the discretized linear viscoelastic spectra are introduced for the description of data.