**System of PDE's Satisfied by the Product**

Computing a system for the product is now a simple call to
__Mgfun[`sys*sys`]__
.

`> `
**sys:=`sys*sys`(sys1,sys2,sys3,sys4,sys5);**

Note that the routine
__gfun[`diffeq*diffeq`]__
performs a similar task, but is restricted to the univariate case, i.e., to functions described by a single ODE. Thus, it can only compute the ODE which does not involve cross-derivatives in the system above, and a similar equation with derivations with respect to
. It turns out that this would induce a loss of information, precluding the following calculation of the integral. Besides,
__Mgfun[`sys*sys`]__
would also deal with systems of mixed differential-difference equations.