  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.
