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In this paper a method for solving operator differential equations of the type X' = A + BX + XD; X(0) = C, avoiding the operator exponential function, is given. Results are applied to solve initial value problems related to Riccati type operator differential equations whose associated algebraic equation is solvable.
In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and further to find...
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