The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients.In fact,we give the general formula for calculating the elements of the matrix e^At.We also give the results when the characteristic equation has the repeated roots.The present method is simpler and better than the other methods.