In this paper, we characterize linear differential operators that. preserve the nth order linear nonhomogeneous systems of differential equations. We first show that a linear differential operator preserves the nth order linear homogeneous system with...
In this paper, we characterize linear differential operators that. preserve the nth order linear nonhomogeneous systems of differential equations. We first show that a linear differential operator preserves the nth order linear homogeneous system with constant coefficients, and extend it to the nth order linear nonhomogeneous system of differential equations with nonconstant coefficients. Then we also show those linear preservers form a monoid, not a group. We also give a necessary and sufficient condition for the linear differential operator to have an inverse.