In J. Jones et al., J. Symbolic Comput. 25 (1998) 99-124, an algorithm for computing the generalized inverse of a singular rational matrix has been implemented in Maple. In this paper, we present a new symbolic algorithm to compute the initial value problem of higher order differential equations with constant coefficients using generalized inverse. The algorithm is subsequently implemented in the symbolic computational package Maple. (C) 2001 Elsevier Science Inc. All rights reserved.