BrzI wrote on Dec 20^th, 2014 at 9:32am:

Sometimes (like 50%of the time) when I engage the autopilot shortly after takeoff it goes into a dive. This will also happen when flaps/slats are up and the aircraft is properly trimmed. Does anybody else have this behaviour ? Is there a way to mitigate this ? Thanks

Turning on your Flight Director after engaging the autopilot should stop this from happening.