الخلاصة

The main aim of this search is to solve kind of partial differential equations of second order with variable coefficients. Where some of and are functions of or both . For this purpose, we willuse one kind of the partial differential equation we found the substitution transformsthe above kind to the first order ordinary differential equation with two independent functions . We found the general form of its complete solution and we appliedthis form for solving the heat equation as physical application insphericalcoordinates