Two methods of integrating the first-order averaged Fokker-Planck (FP)
equation used in the theory of random oscillations are proposed for t
he non-autonomous cases. Further, since the effect of some nonlinear t
erms is lost during the first-order averaging procedure, the procedure
s for obtaining higher approximate solutions to the FP equation are de
veloped. It is shown that these procedures involve the classical first
-order averaging method of coefficients in FP equation. The Duffing an
d Van der Pol oscillations are considered.