According to Apple Music copy rights, you can sync your iphone to only 1 PC. As soon as you try to sync your music library on another PC, you receive a warning that iTune has to delete all media on iphone to be able to sync with this PC.Hmm, just noticed Item 5, my iPhone connects to my Desktop and my main Laptop and syncs with my iPad, not sure why it is only allowing you to connect to only one PC.
This is from iPhone faq:
By design, Apple limits iPhone syncing to one computer. Only one iTunes library can be used to transfer media to and from the iPhone. Attempting to sync the iPhone with a different computer results in a dialog box warning that the iPhone is synced with another iTunes library. The choices offered...
Edit : it seems that Apple doesn't allow syncing iPhone with multiple PCs. You need a 3rd party sync manager to bypass this limit and it's against iPhone policy to use third party sync managers.
If you wish to sync iPhone with multiple computers, then it can certainly be a difficult task. Get best solutions to sync iPhone to multiple computers here.