  We first classify all supersymmetric solutions of the 3-dimensional
half-maximal ungauged supergravity that possess a timelike Killing vector
coming from the Killing spinor bilinear by considering their identification
under the complexification of the local symmetry of the theory. It is found
that only solutions that preserve $16/2^n, 1 \leq n \leq 3$ real
supersymmetries are allowed. We then classify supersymmetric solutions under
the real local symmetry of the theory and we are able to solve the equations of
motion for all of them. It is shown that all such solutions can be expressed as
a direct sum of solutions of the integrable Liouville and SU(3) Toda systems.
This completes the construction of all supersymmetric solutions of the model
since the null case has already been solved.
