Slashdot used to be a safe site to visit, it never made noise when you didn't want it to, making it the go-to site for quiet, in-office news aggregation.
Not anymore. I just had to mute my laptop due to a slashdot auto-playing video advert.
In Tallinn, the ticket inspectors are still there though. And you can get fined if you are a local resident and should ride free, but forgot to "buy" your free ticket by swiping the RFID card in the bus. Even after several court rulings undoing such fines.
However, the idea of free public transport, is not that bad, if feasible. In Tallinn, it used to be heavily subsidized anyway, with only ~20% of the money coming from ticket sales (IIRC). They are also planning to extend this to railways within the city, which are operated by private companies - would definitely make some commutes quicker.
Solving that differential equation analytically (as opposed to numerically) will yield an analytic solution to this problem. Also, accounting for the initial conditions is part of solving an equation. A differential equation itself does not give an answer (neither exact or approximate) - you have to solve it using some method (which can be exact, approximate or numerical).
The right hand side of the closed form solution might also include integration (eg if there are some integrals which cannot be represented using elementary functions), infinite series etc and it would still count as an analytic solution (although I suppose it depends on the exact definition of "analytic solution"), even though evaluating it for some particular point in time (in this particular case) can not be done exactly (you would have to numerically evaluate the integrals etc).
Granted, as has been pointed out, GP has not provided us with an analytic solution to that equation.