The solution of a scalar differential equation is given by the variation of constants formula in terms of any fundamental matrix solution of its homogeneous form and its inverse. We extend this to vector differential equations (both linear and non-linear). It is important to make this inverse as explicit as possible. We do this for vector differential equations with constant matrix coefficients. In addition, we also give new results for the well studied case of a scalar differential equation with constant coefficients.
['Christopher S. Withers', 'Saralees Nadarajah']
Vector differential equations