A generalized Allwright formula and the vector Riccati equation
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2010
 arXiv:
 arXiv:1010.5702
 Bibcode:
 2010arXiv1010.5702M
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 34A34
 EPrint:
 23 pages