Mykhailo Horodnii

The Initial Value Problem for a Higher Order Differential Equation and the Confluent Vandermonde Matrix

abstract:
An explicit formula for solving the initial value problem for a general linear nonhomogeneous differential equation with constant coefficients is given. This formula is obtained using the Vandermonde matrix or the confluent Vandermonde matrix constructed from the roots of the characteristic equation associated with the differential equation.

Mathematics Subject Classification: 34A30, 34A12, 15A21

Key words and phrases: Linear differential equation with constant coefficients, initial value problem, confluent Vandermonde matrix