Random Dynamical Systems of the First Order

The article discusses the method of solving random differential equations of the first order. Random factors cause that only some methods for solving stochastic differential equations enable to obtain efficient results. In addition to the differential equation (together with the initial condition) the output equation should be given. If the output equation is not given, solution of the differential equations are not useful from the viewpoint of the moments of the output process (as opposed to stochastic differential equations in which the coefficients are not random variables). It was assumed that the coefficients are functions of two random variables (A and B) and the force does not contain irregular processes (Winner processes, white and colored noise). The considered equations describe electrical dynamical systems of the first order. The expected value of response of the system, cross-correlation function of the force process and response process and the correlation function of the system response have been determined. It was considered RL series circuit as an example of a solution the problem, where the response is the voltage at the resistance. An example of the problem solution has been presented for a series RL circuit assuming that the voltage across the resistor is the response of the system.