ИСТИНА

In this paper, we deal with a problem of the solutions symmetry for linear matrix time-varying differential equations. Throughout the paper, we assume that the coefficients in the equation are of finite order of smoothness. To verify whether a solution to the initial value problem is symmetric on a given interval, we propose to construct a special matrix sequence. Using the sequence, we prove a sufficient condition for the solution symmetry on a given interval. Under the above condition, we establish a formula for symmetric solutions to linear matrix time-varying differential equations.