regardless of the use you wish to make of the recording it is illegal to make a copy. The owners have copyright and may choose to take action, so be careful.
To answer your question there are various programs which enable you to copy from both DVD's and CD's. I use Nero, which came with my PC package and is relatively inexpensive to buy 'over the counter'.
Some DVD's do have an 'anti-copying' feature built in, if the particular disc you wish to copy from has this feature then you may be out of luck.
There are other possible options...if you know the piece of music by artist and title, you may be able to find in one of the many internet sites, a MIDI version of the music, which is available free (and legal). The music will not be an exact copy of the chosen performance on the DVD, but may be sufficient for your needs.
There are possible legal claims against the producer of the MIDI recordings by the copyright owner, but you will be able to use the MIDI recordings for your purpose, they are normally offered absolutely free for any use.
Of course, you could always do the old-fashioned thing and invite musicians to record the piece of music for you (grab some friends round for a rehearsal, perhaps)
Or even just record the sound on a cassette recorder and then load it to your computer to add to your DVD. A little 'old-hat' but it used to work well enough before all the modern technological stuff superceded it
Anyway, good luck with your attempts, hope you are successful.