(untitled) (Journal of the College of Basic Education, 2022)
Differential equations are used in the study of higher-rank partials with variable coefficients in different areas of the Cartesian coordinate plane, while some scientists and researchers have: N. Rajabov, A. S. Star & F, A Nasim Adeeb Haneen, and others. Accordingly, the partial differential equation, which will be taken from its rank (fourth rank), was studied in this research while its coefficients differ from those of partial differential equations. In the context of that equation, conditions are set for their coefficients to produce a single solution for that partial differential equation in several different cases related to these coefficients. These conditions were summarized in five theories.