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 expAt] . We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than the other methods.