  The paper deals with second order abstract linear partial differential
equations (LPDE) over a partial differential field with two commuting
differential operators. In terms of usual differential equations the main
content can be presented as follows. The classification and invariants problems
for second order LPDEs with respect to transformations \[x=x(\xi,\eta),\
y=y(\xi,\eta),\ u=h(x,y)v(\xi,\eta),\] where $x,y$ are independent and $u$ is
the dependent variable of the LPDE, are considered. Solutions to these problems
are given for different subclasses of non-parabolic LPDE which appear naturally
in the equivalence problem of LPDE. A criterion for reducibility of such LPDE
to LPDE with constant coefficients is offered as well.
