Closed analytical solution of Riccati type matrix differential equations (Q1194632)

For a nonsymmetric matrix Riccati differential equation with an invertible matrix coefficient in the quadratic term, an explicit formula describing the solution in a neighborhood of an initial point is derived. The result supplements that of the authors published in [Appl. Math. Lett. 4, No. 2, 17-20 (1991; Zbl 0733.34003)]. As in that paper, a special exponential representation of the solution of a Cauchy problem for a second order linear stationary matrix differential equation is utilized.