On a System of Differential Equations with Random Parameters

An explicit formula for the mathematical expectation and second moment functions of a solution to a linear system of ordinary differential equations with a random parameter and a vector random right-hand side is obtained. The problem is reduced to the deterministic Cauchy problem for systems of linear partial differential equations of the first order. We obtain an explicit formula for a solution of linear systems of partial differential equations of the first order with constant coefficients. An example is given showing that random factors can have a stabilizing effect on a linear system of differential equations.