737 can fly a track automaticly, but it takes some fiddling.
You go to position page, copy the present position to the scratch pad, insert the position as the first waypoint on the legs page. Copy the new waypoint to the scratch pad, write the desired track after the waypoint and a forward slash and with an arbitrary distance (or if ATC will be so kind to inform for how many miles to maintain the track). Insert the scratch pad entry as a waypoint and you are good to go.
Takes 10 seconds if you are familiar with the way of doing it. It's a trick and not a documented procedure, hence not something everyone knows.