Solving symbolically a system of 16 equations with 16 boundary values

I'm trying to calculate and plot the deflection (by quadruple integration) for this beam:

and after trying several different approaches I'm forced to ask for help 🙂

When I'm trying to calculate the deflection for each part of the beam separatly it works well, but as soon as i try to do it for all 16 boundary values it just stops cooperating. I suspect that I'm making some dumb error somewhere, but I just can't find it.

Any help would be highly appreciated.