Shakes when accelerating

Please be more specific. Do you feel this in the steering wheel, or does the entire vehicle shake? If it is the entire vehicle, drive at that speed, then when the shaking starts, hold the accelerator pedal and road speed perfectly steady, then briefly tap the brake pedal with your left foot. If the shaking stops for two or three seconds, then starts up again, it is most likely related to the transmission has the wrong type of fluid in it.

If you feel this in the steering wheel, the better suspect is a worn inner CV joint. The clue is that will only cause the symptom during periods of high load/acceleration, but you will typically also feel it at lower speeds than what you described.