Comments on Lagrange Partial Differential Equation

Abstract

The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products consisting of a scalar function, a homogeneous first order differential operator and the reciprocal of the scalar function. The factorization procedure is utilized to show that all totally linear differential equations of first order can be transformed to each other, and in particular to a homogeneous one.