How can I download music from my iPhone without purchasing

See Sync your iPhone, iPad, or iPod using iTunes on your computer - Apple Support.

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If you want to download music from the iTunes Store you will have to buy the tracks/albums.

If you want to subscribe to Apple Music you might have an option to have a three month free trial with it after which it will become paid for (though you can cancel the subscription before it becomes paid-for, and obviously therefore lose access to any tracks downloaded from it)