Based on this statement:
the flexible tube in the output of the boiler burst. ...
The hot water stopped spraying after I closed the water supply.
I suspect the pressure inside the tank has run down through the crack in the hot water flex pipe. I believe it may be possible to replace the flex pipe without draining the tank (if the tank hasn't drained itself already).
Water heaters are sealed units, so if the cold water is kept off, the water should tend to stay inside the tank, similar to how one can lift a straw-full of liquid out of a cup by plugging the top of the straw.
I would also suggest a suitable quarter-turn valve (if your local code allows it) on the hot water side, just like the cold water side, so this sort of repair will be easier next time. Then you could merely turn the hot and or cold valves off on both ends of the flex pipes, then replace the flex pipes easily.
Stand by with a bucket capable of holding the contents of the water heater, in case the water is not held inside. Even if it is held inside, a small steady drip could happen.
If you can use another valve, remove the flex pipe, then attach the valve according to instructions, with suitable sealant if instructed. Have the valve open while attaching it, so the leaking water (if any) flows through the valve and doesn't get in the way too much while threading the valve on. Once the valve is on, close it, then attach the new flex pipe at your convenience.
If you cannot use the extra valve, replace the flex pipe according to instructions.
Filling afterwards: Remove aerators from the house faucets, so dislodged gunk in the pipes doesn't block the faucets. Turn on all valves at the heater, and and a hot water faucet (perhaps all the hot water faucets in the house). Let the water run, and let air bubbles clear through the plumbing. Once no air bubbles appear, start the heating system in the heater.