  In this paper we describe the integral transform that allows to write
solutions of one partial differential equation via solution of another one.
This transform was suggested by the author in the case when the last equation
is a wave equation, and then it was used to investigate several well-known
equations such as Tricomi-type equation, the Klein-Gordon equation in the
de~Sitter and Einstein-de~Sitter spacetimes. A generalization given in this
paper allows us to consider also the Klein-Gordon equations with coefficients
depending on the spatial variables.
