Vibration in my steering wheel, and gas pedal when accelerating

I noticed after getting up in speeds of about 100 mph last week that now every time I accelerate I have a vibration coming through my steering wheel, and gas pedal. The vibration starts around 30/35 mph and gets slightly worse until about 60 mph. The vibration is not so bad that the vehicle can't be drove, but it's not normal. I have had the wheels, and tires looked at, and everything was fine with that. Also a front end shop lifted it up, and told me my front differential, and left axle is bad, and needs replacing. I can believe the left axle part, but as far as in the front diff being bad, I doubt it. That's just a guess coming from the mechanics! I have no symptoms of a bad front diff as far as I know, from looking it up. The vibrations stop when I'm at a constant speed, and no vibrations at all when I step on the brake! Vibrations are the only thing I feel, no noises at this time. What could be the cause? I know an unbalanced drive shaft, motor mounts, CV joints, axle, & U-Joints could all be a possible culprit, but none of this was mentioned by the shop.

2000 Ford Explorer V8 5.0 AWD

Ask, family, friends, coworkers if they have a mechanic they trust and go see one. The only way to tell is to have someone look at it

Have your tires check for Balance and check your fuel filter.