What I've got is a script that runs every three minutes using a line in crontab
*/3 * * * * /home/dougie/dnso.sh
This ugly bash script gets my public IP address using the OpenDNS service then drives the No-IP updater. It logs every IP address when it changes (I've got a record of 303 addresses since 8th Jan 2015). You'd need to kickstart it with echo "192....
This is more a general Linux question as NO-IP clearly document their api and have full install details for the Linux client at this page
Personally I would check your router to see if that does an update - lots of them do and you need to be in the set-up to set the port forwarding.
Once you have followed these instructions, then their support states:
Thanks to @Jaromanda X.
Using user in fstab implies noexec, so add exec after user:
/dev/sda1 /mnt/hd auto defaults,user,exec 0 1
However if you do not want to mount with exec flag you can run:
$ sh start.sh
(or another script interpreter).
As the script is just a text file and the interpreter is on another partition (exec-able), it will run.