How can I get iTunes to load all my music from my library to my iPhone 5? It keeps telling me some songs are not authorized although I purchased them from the same computer.

When I sync my phone with my library iTunes will not copy some songs to the phone, telling me the computer is not authorized for those songs, and instructing me to authorize the computer. I follow the steps to authorize it, to which it responds that it is already authorized. I also recently did a systems update, but still cannot sync these songs. I bought these songs from iTunes on this computer.

I tried the answer of removing my password, deleting my songs from the phone and then trying to re-sync them, but came up with same problem.