Your physician can force the hospital to keep you longer and they can also have you discharged from the hospital when you're well enough to leave the hospital.
However you're free to leave the hospital at anytime without being discharged if you'd like.
No hospitals can force you to stay in the hospital longer than you need to or want too.
So even if you're not entirely recovered from whatever illness or injury you sustained you cannot be forced to stay in the hospital.
You can walk right out the doors of the hospital if you want and no one can legally force you to stay.
Now there's an exception the hospital can require a minor to stay in the hospital until discharged and could stop the minor from leaving without the parents consent.
But if the parents are there then the parents can legally remove the child or minor from the hospital if they want too and no one can stop them from doing so.