ISSN: 1813-0410

Author : Hadi Hanoon, Wafaa

The Solution of Special kind of Linear Second Order Partial Differential Equations and Solution The Heat Equation as Physical Application in Spherical Coordinates

Ali Hassan Mohammed; Ali K. Hasan; Wafaa Hadi Hanoon

journal of kerbala university, 2012, Volume 8, Issue 2, Pages 291-303

The main aim of this search is to solve kind of partial differential equations of second order with variable coefficients, which have the general form

where some of and are functions of or both .
For this purpose, we will use one kind of the partial differential equations its formula
where are real constants.
We found the following substitution
Transforms the above kind to the first order ordinary differential equation with two independent functions , which have the general form

We found the general form of its complete solution and we applied this form for solving the heat equation as physical application in spherical coordinates