Help with system of equations.

HI guys,

It's been a while .

I've got a question, if someone could help it'd be nice.

The thing is this: in the attached files there is a system of equations solved. The system has some variables which in term are functions (of some sort) and I can't see how or even why there were some solutions found and besides what exactly are these solutions? At first they seem to be integers but somehow he made them functions of t?!

I've searched the internet (PTC community including) but I couldn't find something that did explain the way Mathcad solves these kinds of equations!

Thanks for any replies.