Hi guys,
It must have been at the very least a decade or two since the last oil change, as the old oil draining from the diff was very dark brown. I filled it with 80W-90 API-GL-5 gear oil as stated in my owner's manual. The diff is a 3.91 on a 740GL.
A day or two later the diff starts to whine very noticeably and gets louder as the RPMs go up. The whine is most noticeable with a combination of higher revs + no foot on the accelerator. Put the foot down just a bit, and the whine mostly goes away.
For example, it's very noticeable if you're going 3.5k ish in 3rd and let go of the accelerator completely. Whereas if the revs are lower then its not heard unless you listen closely.
What could this be? The oil i put in is a mineral Nulon 80W-90.