1 - Create a CNAME record from 'www.mywebsite.com' to 'dynamic.mywebsite.com'.
2 - Point your A name record from 'website.com' to '18.104.22.168' which is the wwwizer.com service. It will redirect your website.com to www.website.com that points to your dynamic IP.
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.