English

A generalized Allwright formula and the vector Riccati equation

Classical Analysis and ODEs 2010-10-28 v1

Abstract

A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation, and in a similar way the generalized formula is connected with a special type of a differential system called a vector Riccati equation. Moreover,the classical result that a scalar differential equation is a Riccati equation if and only if its general solution is a fractional linear function of the starting value, is also generalized to a differential system.

Keywords

Cite

@article{arxiv.1010.5702,
  title  = {A generalized Allwright formula and the vector Riccati equation},
  author = {Kurt Munk Andersen and Allan Sandqvist},
  journal= {arXiv preprint arXiv:1010.5702},
  year   = {2010}
}

Comments

23 pages

R2 v1 2026-06-21T16:34:58.272Z