This extension is often necessary for solutions to exist, and it also results in
more physically reasonable properties of solutions, such as possible presence of
shocks for equations of hyperbolic type. Several authors studied the solutions
of linear differential equations and system of differential equation but they
used different methods, see[1 − 5] .In the present work we find the solution
of (2×2) and (3×3) systems of first order nonhomogeneous linear differential
equations using new technique which defined in section two .