Thanks for the elucidation!
What if " x " is an N-dimensional column vector and A a matrix multiplier OPERATOR and the BOTH of these are FUNCTIONS of the TIME " t " in the Linear, homogeneous case. Thus
dx(t)/dt = A(t) x(t) .
The Matrix operatorS (plural) A(t) may not commute among one another at different times. Then, are there any methods to crack this problem besides the Dyson Chronological operator way by refined time-slicing? What if the elements of A are analytic functions of the time variable t ??? Could one, then, express the equation as the log-derivative of of x(t) equaling A(t) and integrate in a straightforward way with the initial vector x(0) given????