Why doesn't some songs show up on my Iphone?

I downloaded some songs from a website and I did everything to put it on iTunes. Now the thing is that it shows up on iTunes but it doesn't show up on my phone even when I try to sync it.

Then don't sync. Use manual management mode in iTunes. It works on all Apple devices that I've used - from Nano 1st gen to iPhone 5, and both iPod Touch 3 and 4. Manual Management is clearly superior to syncing in every way. I've never had this problem.

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