Abstract
In this paper we describe the integral transform that allows to write solutions of the time-dependent partial differential equation via solution of a simpler equation. 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.
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