  An affine factorable surface of the second kind in the three dimensional
pseudo-Galilean space G13 is studied depending on the invariant theory and
theory of differential equation. The first and second fundamental forms,
Gaussian curvature and mean curvature of the meant surface are obtained
according to the basic principles of differential geometry. Also, some special
cases are presented by changing the partial differential equation into the
ordinary differential equation to simplify the solving process. The
classification theorems of the considered surface with zero and non zero
Gaussian and mean curvatures are given. Some examples of such a study are
provided
