Solving an implicit second order differential equation matrix with numerical data

So, here's an abridged version my problem (see attached file ODELoop1.pdf). I need to solve a second order differential equation under the form of a matrix. At first, I tried going fully symbolical and using dsolve, however I always got the message "Warning: Explicit solution could not be found." (which means that Matlab isn't able to isolate each of the components of the vector theta, right?). So now, I'll try with numerical data.

I was wondering if any of you know some way to solve my ODE (no need to give me the whole solution, just tell me “Have you tried this thing?”). If that’s any help, I’ve also joined my Matlab Code (BoucleForGrosseMatrice) as well as an entirely symbolic version of said code (CalculRapid) as well as the full calculation behind my code (Demarche.pdf). In my main code, the part that I’m stuck at is identified as “ THIS SECTION!!! HERE!!! ” (it's near the bottom of the code).

One last thing, sorry in advance for all the French words in my files...