Precise solutions of the stationary Fokker-Plank-type equation are obt
ained in quadratures for two- and three-dimensional electron gases. Th
ese solutions relate only to the case when electron-electron interacti
on is omitted. To illustrate our method we consider the example of the
interaction of electrons with optical phonons at high temperatures wh
ere the approximation of small-angle scattering is appropriate. Compar
ison of mobilities calculated by our method and the obvious tau approx
imation gives the divergence only in numerical multiplier.