Running two different sql servers?

On my personal computer I am running Mysql on the computer at work we are running Sybase sql anywhere. I am having a horrible time figuring out how to use the user interface for sybase (the only reason it is on our server is that another program we use uses it). I was wondering if there would be any major conflicts with running both sybase sql anywhere and mysql on the same computer.

Thank you in advance for your help

As usual, "it depends". Two databases in one server is generally better than two servers, because the RAM cache will be shared. If one database goes quiet, and the other one is heavily used, the cache will be used efficiently.
With two servers come two caches, and the quiet database's cache wil just sit there wasting space that could have been used by the busy database.

How's your server specs? Sometimes 2 databases are just too hot to handle for server. It's better if both databases have the same page size, since the page frame size used by the server must equal the largest page size of the two databases.

If you're the only user using the other DB, I don't think you'll be starving your sybase db of its resources. But how's your sql or security team feal about that? I'd get slapped on the wrists for that....