Sorry to tell you this, but I'd get it to a shop ASAP which can diagnose it. It sounds like you have a transmission problem. When the transmission fails it defaults to being locked in 2nd-gear which is called "limp-home" mode.
The engine is turning more revolutions at the lower gear. Once you shift into a higher gear the rpms drop.
take tranny apart and replace 5th gear syncro
The first cause of the jump out from one to other gear is the loose shifter fork, which connects the shifting linkage and gears of the transmission. The second cause is loose shifting linkage itself, which connects the gear shifting knob and shifting fork. The shifting linkage and shifting fork become loose due to the rapid changing of gears from one gear to other at high speed of vehicle. The third cause is the misalignment of shifting linkage to the shifting fork.
On the transmission!!
I can only assume that this is in reference to the gear shift on the 2002 Odyssey. I had to ask a dealer mechanic, who had to play around with the shift lever, before finding out it was just how it was made. When shifting normally, one has to pull the shift lever TOWARDS you and then move it up or down to the top gear positions (P, R, D, N). In those cases, you would be applying brakes and not moving. When shifting in the lower drive gears you can be moving, but you need to push the gear shift lever forward, or away from you and move it to the approppriate lower gear (2, 1, etc.). I hope this answers the question.
D3 will hold the transmission in 3rd gear not allowing it to shift to a higher gear.
First guess I'd say your transmission is not shifting into a higher gear.
well yes and no, you will need it to pull out from a stop unless you can crank the engine to get moving or your gonna pop start it every time, also for shifting gear, you can shift without the clutch if you know what your doing, but it will shorten the life of the transmission,
Have the trans computer checked for codes. The tcm will have set a code.
While driving my cavalier will shift into high gear for at least a couple of minutes. Shifting gears,giving it gas does not help. Any suggestions?
Trouble code P0730 means:Incorrect gear ratio
It could be starting in a higher gear. You need to have it checked for trouble codes.