Constructive solution of the Cauchy problem for a special class of partial differential equations with constant coefficients (Q1901220)

This work is a further development of the author's previous investigations. A method for constructing solutions to a special class of linear partial differential equations with constant coefficients (in two variables) is proposed. A Cauchy problem in the homogeneous case is formulated and a method of solving it is presented. Solutions in the form of formal series or polynomials are found. No convergence of the series-solutions obtained is considered here.