Matrix Differential Operator Method of Finding a Particular Solution to a Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

Abstract: The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special types of the right-hand side. Calculation requires the determination of an inverse or pseudoinverse matrix. If the matrix is singular, the Moore-Penrose pseudoinverse matrix is used for the calculation, which is simply calculated as the inverse submatrix of the considered matrix. It is shown that block matrices are effectively used to calculate a particular solution.