If you're not interested in installing a new app than youtube, just go away then, because we need a new app. - Go to appstore

Go to search

Search for "jasmine"

Install Jasmine

Click on your new app "jasmine"

Search for a song

I'm finding a Rascal Flatts song

The song "The broken road"

It is playing now

Leave the app, and double click on your home button so the multitaske bar comes up, then scroll to the left till you find the Jasmine app and pause button, and then press play

Now it is playing then press the home button again.

Lock your phone and it is still playing. Double click on the home button to pause it.

Hope the tip helped you a bit. If it is possible on the Youtube app in app store,, my mistake then. My iPhone language is in Danish, if it confuses you I'll change the pictures. Twitter: @neklasd

UPDATE! iTube is a better choice, since Jasmine doesn't properly work in iOS 6.1

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