Singular Generalised Autunomous Linear Differential Systems
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006We produce a parallel algorithm realizing the Laplace transform method for the symbolic solving of differential equations. In this paper we consider systems of ordinary linear differential equations with constant coefficients, nonzero initial conditions and right-hand parts reduced to sums of exponents with polynomial coefficients.
Sufficient conditions for the -th order linear differential equation are derived which guarantee that its Cauchy function , together with its derivatives , , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.