matrix_riccati(A, K, Z0, t)

matrix_riccati(A, K, Z0, t=t0)

matrix_riccati(A, K, t)

matrix_riccati(A, K, t=t0)

The unknowns are

A simple example would be

The matrix with the initial values  and  is

The system of equations represented by these matrices is thus

The two coupled odes are

The matrix solution to this matrix system of equations with initial conditions  at  is computed as:

Recalling the form of , the solution to the system of odes is constructed from  as

This result can be verified with odetest

dsolve, odetest, riccati_system, riccatisol