  We present the exact time-dependent solutions on inhomogeneous spherically
symmetric space-time in the conformal invariant Weyl gravity. For this purpose,
the subclass of the Lemaitre-Tolman metric which is supported by an anisotropic
fluid is used. For the first time, the exact solutions of the dynamical
equations are obtained for two special cases. One of the exact solutions is a
de Sitter space-time and other solution is a class of time-dependent wormhole
geometries which can be supported by exotic matter in similar to the general
relativistic solutions.
