riccati_system can find a closed-form solution for certain systems of riccati ODEs. A system of riccati ODEs of n variables is:

with initial conditions

where  are the unknown functions and  are polynomials in  of second degree with function coefficients.

To solve this system, riccati_system tries to convert it into a matrix equation,

with

where , and  are n by n matrices. The user can request this matrix form instead of a full solution by using the 'matrix_only' option. In this case a sequence  is returned.

This function is part of the DEtools package, and so it can be used in the form riccati_system(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[riccati_system](..).