In the paper, the system of equations of the laminar boundary layer for the case of a "frozen" flow of dissonant gas was brought to a universal form in the sense of Lojcjanski's definition, with the help of expedient transformations and a suitable set of parameters. The numerical solution of the obtained system of universal differential equations was performed, according to the known methodology, by the finite difference method. The results of the calculations are shown on the attached diagrams, based on which conclusions were drawn about the influence of the compressibility parameter $f_0$ on the characteristic sizes of the boundary layer. Based on that, a general conclusion was made about the justification of localization of the boundary layer equations according to the compressibility parameter $f_0$.