When I posted this I never imagined that it would require so much work to solve.
Neither did I ;-)
I just figured I was doing something wrong, not because Mathcad couldn't do it.
It was both - units and IC on your part, not accepting vector equation and more than one highest derivative in one equation (at least I guess that was the problem - not sure if thats a general rule) on part of Mathcad.
The problem was exciting to me as it looked like a simple task at first and with ever step it seemed that the file now should work bit it didn't even though I thought it should: first the correction of the units and the superfluous ICs, then making three separate equations (there must be a bigger mistake in that file than just missing the kN but I didn't kept the calculations and now it doesn't matter anyway).
I'm still a bit disappointed about the limitiations of Prime's (and Mathcad's) odesolver which prevent a natural and convenient solution.