  This paper studies exact meromorphic solutions of the autonomous Schwarzian
differential equations. All transcendental meromorphic solutions of five
canonical types (among six) of the autonomous Schwarzian differential equations
are constructed explicitly. In particular, the solutions of four types are
shown to be elliptic functions. Also, all transcendental meromorphic solutions
that are locally injective or possess a Picard exceptional value are
characterized for the remaining canonical type.
