How do I solve a matrix of ODE equations?

I have developed some Simulink code that displays the primary and secondary (referred to the primary) current on a scope. The results are as expected.

I used Faraday's Law and Flux Linkage equations to determine the equations and block flows.

Instead of using the block flow method shown above, I would like to solve this problem using the matrix of ODE equations shown below. How would I utilize this matrix below to simulantenously solve my two differential equations. Utilimately, I will have six equations. If I can solve just the two equations first I can match the answer with the code above to ensure I get the correct answer. The dash above the variables in the second row means referred, it does not mean derivative.

Answer 1

[Torsten]

Your system reads

M*dz/dt + F*z = R

or

dz/dt = inv(M)*(R-F*z)

It should be easy to solve using "ode45", e.g.