A generalized Allwright formula and the vector Riccati equation

Details A generalized Allwright formula and the vector Riccati equation A generalized Allwright formula and the vector Riccati equation

2010-10-27

arxiv.org/abs/1010.5702v1

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

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.

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