Extract in part from the B737 Classic Boeing Flight Crew Training Manual under sub-heading "Initial Climb - One Engine Inoperative>
The initial climb attitude should be adjusted to maintain a minimum of V2 and a positive climb.....if an engine fails at an airspeed between V2 and V2+20, climb at the airspeed at which the failure occurred. If engine failure occurs above V2+20, increase pitch to reduce airspeed to V2+20 and maintain until flap retraction altitude....if obstacle clearance requires a special engine-out procedure and immediate turn is required...initiate the turn at the appropriate altitude (normally at least 400 feet AGL). Maintain V2 to V2+15 with take off flaps while manoeuvring...after completing the turn and at or above flap retraction altitude accelerate and retract flaps.