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

Doniyor G’afurovich Rayimov

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

Authors

Doniyor G’afurovich Rayimov PhD, Associate Professor, Department of General Technical Sciences,Asia International University

Keywords:

For example, among the examples given above, the first and the fourth are first-order linear partial differential equations.

Abstract

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.

References

Salokhiddinov, M.S. Equations of Mathematical Physics, Tashkent: “Uzbekistan”, 2002.

Mixlin, S.G. Course of Mathematical Physics, Moscow, 1968.

Sobolev, S.L. Equations of Mathematical Physics, Nauka, Moscow, 1966.

Bitsadze, A.V. Equations of Mathematical Physics, Moscow, 1976.

Bitsadze, A.V., Kalinichenko, D.F. Collection of Problems on Equations of Mathematical Physics, Moscow, 1977.

Downloads

Published

2026-05-18

How to Cite

Doniyor G’afurovich Rayimov. (2026). FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD FOR SOLVING THE CAUCHY PROBLEM ASSOCIATED WITH THEM. Ethiopian International Journal of Multidisciplinary Research, 13(5), 1147–1149. Retrieved from https://eijmr.org/index.php/eijmr/article/view/6825