Using a program of symbolic calculation, we can determine, in a relatively easy manner, the unique scalar third-order partial differential equation, whose symmetry group includes Aff(3). Unfortunately, the derived form does not say anything about the structure of the differential equation, apart from the fact, that it is Aff(3)-invariant. I will show that an appropriate geometric approach allows for the determination of the differential equations more easily, finding as a by product, some new and unexpected properties of such a differential equation that can be difficult to be found by calculations.