Easier solution:
1 - Create a CNAME record from 'www.mywebsite.com' to 'dynamic.mywebsite.com'.
2 - Point your A name record from 'website.com' to '174.129.25.170' which is the wwwizer.com service. It will redirect your website.com to www.website.com that points to your dynamic IP.
Best solution:
Not all domain registrars allow you to set you base host as a CNAME, the problem is:
A points name to IP
CNAME points name to name
If you can't point your A to an IP because it's dynamic and you can't point website.com to a name due your domain registrar limitation. How will you point to your domain to the dynamic IP?
I suggest you to use cloudflare as far as I can remember they accept you to set your base domain as a CNAME. Follow these steps:
1 - Create your account in https://www.cloudflare.com it's a free CDN (content delivery network) you'll be able to just use the DNS service if you want.
2 - Change your nameservers to cloudflare.
3 - Wait the DNS propagation time (24 hours) and check if cloudflare is working. (It shows in your cloudflare dashboard)
4 - Point 'website.com' to dynamic.website.com then point 'www' to 'website.com'.
Hope it helps.