Solvability of infinite differential systems of the form x′(t)=Tx(t)+b where T is either of the triangles C(λ) or ¯¯¯¯¯Nq

In this paper, we are interested in solving infinite linear systems of differential equations of the form x′(t)=Tx(t) +b with x(0)=x0; whereT is either the generalized Cesàro operator C(λ) or the weighted mean matrix ¯¯¯¯¯Nq,x0 and b are two given infinite column matrices and λ is a sequence with non-zero entries. We use a new method based on Laplace transformations to solve these systems.