"FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD FOR SOLVING THE CAUCHY PROBLEM ASSOCIATED WITH THEM"

In this topic, we study first-order partial differential equations, including their quasilinear and linear forms, as well as homogeneous and non-homogeneous types. We also discuss methods for constructing both particular and general solutions of these equations using their characteristic equations and families of characteristic curves, known as first integrals. Furthermore, we examine how to determine the solution of the Cauchy problem posed for such equations based on the obtained general solution.