A Learjet on a Tower controlled IFR flight suffered an NMAC with a commercial B737-700 departing from their destination airport which turned toward them rather than flying runway heading as directed by their takeoff clearance.

Narrative

I was cleared for take off from SADF airport from Runway 05; cleared to fly runway heading; climb and maintain 1;500 FT contact SABE Tower. As soon as we contacted the Tower [they] said; 'Continue climb to 3;000 FT on heading 050'. Then; a few seconds later; said; 'turn right direct to PTA VOR climb and maintain 4;000'. At this time commercial traffic was cleared to takeoff from Runway 13 from SABE. Their clearance was; 'cleared for takeoff Runway 13; climb to FL050 direct to PTA VOR'. One and a half minutes later we received a TCAS TA and as soon as we checked the instrument and looked outside received a CLIMB; CLIMB; CLIMB resolution advisory. I simultaneously disconnected the autopilot and followed the resolution directive. 10 to 15 seconds later TCAS announced 'clear of conflict' and my First Officer spotted the B737-700 at no more than 100 meters during our evasive maneuver. The commercial aircraft had turned 90 degrees left of their assigned heading after take off and never took evasive action.