Yes, he wrote both of them. The drums and bassline, however, may have been done by his bandmates, although Kurt would often write their parts for them as well.
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One of the last books Kurt Cobain read was The Beautiful and the Damned by F. Scott Fitzgerald... i think.. i read it in Who Killed Kurt Cobain.
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what are the lyrics to the song"...to write the love of God would drain the oceans dry.
Probably not. I say 'probably' because it could be possible that Cobain did a lot of work with her on the songs and influenced her to edit and change many of them. Actually, this is quite possible, since her best CD "Live Through This" was released/made when Courtney was with Kurt. Not to say that she isn't talented, but Kurt was extremely musical and had amazing abilities to fine-tune songs. He was an artist. And Courtney probably used him for editing/advice on her music, maybe to even write a few lyrics. But no, I wouldn't go as far to say, 'Kurt wrote the entire album and she's a liar'. There's definitely Courtney in that particular album.
Much of Kurt's music was a mix of depression, angst, and his negative views of many things in life. The lyrics to many songs can be interpreted in different ways by different people.