  We present some exact solutions of relativistic second-order hydrodynamic
equations in theories with conformal symmetry. Starting from a spherically
expanding solution in ideal hydrodynamics, we take into account general
conformal second-order corrections, and construct, for the first time, fully
analytical axisymmetric exact solutions including the case with nonzero
vorticity. These solutions are time-reversible despite having a nonvanishing
shear stress tensor and provide a useful quantitative measure of the
second-order effects in relativistic hydrodynamics.
