[en] One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system can be described by equations similar to Mathieu equation with account of stochastic forces. Such equation is studied by analytical approach. The solutions for higher order of accuracy are obtained. The method for numerical solution and resonance zone detection is proposed. The solution for the extended Mathieu equation is obtained for wide range of parameter values. The results of numerical solution are compared with analytical solutions of different order and known analytical results for Mathieu equation. (paper)