ma7 wrotebuy/move your example.cm domain from no-ip.com or dydns.com and configure your router (or any computer behind it with a client installed) to automatically update the example.com A record to point to your new allocated IP everytime it gets changed.
Exactly. It's best if your router supports this even if you have to buy a new one.
But it should be possible for the computer to update the DNS automatically, in theory at least. The thing is the computer will not get a notification when your IP address changes so it has to check all the time.