At present there is not a free tier of Dyn DNS services, however a 7 day trial is available at no cost to you to try it out. To sign up for this trial, visit dyn.com and click on the "try Dynamic DNS" button. This will then take you to the cart to complete your transaction and create an account in the process. So long as you cancel before the trial is complete you will not be charged. If you do not cancel, your card used to sign up will be charged for a year of service.
Oracle + Dyn