journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2559 Solution of special cases of PDEs with homogeneous terms Ketab Sattar Naser Department of Mathematics, Faculty of Education, University of Kufa, Kufa, Najaf, Iraq Abdullah Banen Wafaa Department of Mathematics, Faculty of Basic Education, University of Kufa, Kufa, Najaf, Iraq Mousa Zainab Radhi Department of Computer Science, Faculty of Computer Science and Mathematics, University of Kufa, Kufa, Najaf, Iraq 29 5-B 1663 1670 27 06 2026

This study seeks to derive complete solutions for certain classes of third-order linear partial differential equations with constant coefficients involving three independent variables, expressed in the general form: B1 Hppp + B2 Hppn + B3 Hpnn + B4 Hnnn + B5 Hppm + B6 Hpmm + B7 Hpnm + B8 Hnnm + B9 Hnmm + B10 Hmmm + B11 Hpp + B12 Hpn + B13 Hpm + B14 Hnn + B15 Hnm + B16 Hmm + B17 Hp + B18 Hn + B19 Hm + B20 H = 0. Based on this supposition, the above equation can be simplified to a third-degree nonlinear second-order ordinary differential equation with three free functions.

 Partial differential equation Ordinary differential equations Complete solutions access open retracted no