The conventional approach to the modelling of semiconductor devices operation is based on a numerical solution of transport equations. This paper exposes a complete analytical treatment of transport equations for a two-valley semiconductor. We consider the case when the geometry of the analysed structure permits us to assume that the transport in one of the dimensions of the structure is dominant, and when the electric field is homogeneous and stationary. The obtained solution for the case of generally set initial conditions is reduced to the quadratures. We used the example of a p-i-n diode to demonstrate the superiority of the analytical treatment as compared with the numerical one. The proposed approach offers the possibility to determine exactly and quickly the spatial-temporal distribution of the electron concentration within the structure. Considering the accuracy of the analytical procedure, compared with that of the numerical one, the obtained solution could also be used as a kind of standard for the analysis of particular approximate solutions of the considered type of partial differential equation systems.