Here is a simple way to save music from Youtube on your iPhone, without running into trouble.
There just two methods to do this, we either do this with an application or we use converters that are mostly online.
Apps
If we are using an application, then we need an application that not only downloads, videos but converts then to MP3 even before it downloads.
Tubemate comes to mind, with tubemate you can download any Youtube video in any video format, it is also a powerful MP3 downloader.
Tubemate is not available in the store, so you have to download it here HERE
Once downloaded, install it, then open it up, if you used to downloading things online, using Tubemate will be easy for you.
Converters
This online downloaders requires only the Youtube web address of the video, once you paste it in any of the converters cum downloader, select the format and the quality then hit convert and download.
It will then save the Music on your iPhone.
For a list of recommended online down loaders see here. Otherwise you can search on google for one.
Watch the Video