Have a Honda 2006 CRV 89K miles. When I start the car put it into drive first time at or near to the first gear change point get a thud sound (sound from the rear, maybe left rear as face vehicle). However as drive the car around coming to a stop without turning off the vehicle, on acceleration no sound. If I park the vehicle on restart and acceleration get the same sound but depending on the amount of time the vehicle is out of gear the sound seems to be lessened (less time less sound). Help with any hypotheses would be appreciated.
Is your car FWD? Or is it RWD, & configured w/ a driveshaft between the engine and a rear differential? If the latter, any play in that could cause this symptom. This is a pretty common symptom for certain GM trucks as I recall, caused by lack of lube (or wrong type of lube) in the two-part splined-driveshaft joint. If this is the cause, it usually makes a thunk when stopping too.