Battery explodes

That would be a sure sign that it is overcharging the batteries and literally boiling the electrolyte out of them. First thing I would do is run a test on the charging system. The generator could be dumping a higher voltage than needed.
If it has dual batteries they need to be the same exact size and type. Be sure to have both tested because one side could be faulty and causing the generator to see a low battery and keep charging when it is actually a bad battery.

Thanks so much. I will talk to son as soon as possible, and hopefully, he will have saved enough money to take it to our local mechanic to have it tested. Have a great week!

If he has a multi-meter with a voltmeter he can test it himself. Tell him to attach the voltmeter to the battery with the positive (red) voltmeter test lead on the positive battery post and the negative (black) voltmeter test lead on the negative battery post, get a reading on the DC volt scale, write that down, then start the engine rev it up to 2,000 rpm and read the voltmeter again. The seconds reading should be more than 0.5 volts than the first reading, such as 12 volts with the engine off, then 12.5 volts with the engine running at 2,000 rpm although normally the voltage at 2,000 rpm should be slightly over 14 volts. If it is over 15 volts, then I would have him remove the alternator, take it into a auto-parts store for a free bench test to make sure it is not a faulty alternator and/or a stuck voltage regulator.
You should mention what engine this is, too.