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Русская версия

**L. V. Linchuk**

Russian State Pedagogical University

Saint-Petersburg

Russia

lidiya@p110.f289.n5030.z2.fidonet.org

Last researches have shown that we can considerably expand
classes of symmetries investigated in group analysis
using formal approach.
In this paper the main ideas of theory of formal operators are spread
on the space of three variables x, y, w, and then we proved
the fundamental principle of symmetry analysis of the generalized
differential equations
*y ^{(n)}=F(x,y,w,...,w^{(n-1)},
y^{(n-1)},w^{(n)})*
– principle of factorization.
In particular, this class includes
functional differential equations, therefore the approach
can be applied for search of factor system and precise solutions of these
equations.
The main part of the paper is devoted to research
of base of invariant space of admitted operator and algorithms of its search,
as these ideas allow to spread principle of
factorizations on the class of generalized differential equations.
We considered the most perspective classes of operators defining
the given type of factorization.