How to symbolically solve a system of ODEs with general time dependent matrix coefficients?

I have the following system of ODEs

where Q and A are 3x3 matrices, and the b is a 3:1 vector.

[darova]

It's impossible. Use numerical approach ode45

[Mirlan Karimov]

I realized it little after dropping the question here. Thank you anyway!

Answer 1

[Mirlan Karimov]

As there is no closed form solutions to such general problems, it can be solved only numerically.