It is known that a lot of mathematical calculations must be processed during a practical use of exact and approximate methods, which are designed to analyze random phenomena in nonlinear dynamic systems. The present paper describes some schemes of such analysis. These schemes expect an application of a computer algebra system (CAS) Mathematica v. 4.1 [9], which is a very powerful and suitable tool for above mentioned topic. At first, relations between moments, cumulants, and quasi-moments are derived. Further, a problem concerning the seach of polynomial stochastic potentials is considered. Necessary conditions and relations are obtained to solve the last problem. All calculations of appropriate expressions were produced with the help of our package ProbRel and different procedures.