ISSN: 1813-0410

Author : Hassan Mohammed, Ali

"Finding the complete solution of special types of the second order partial differential equations with variable coefficients"

Ali Hassan Mohammed; Mohammed Monther Neamah Kudaer

journal of kerbala university, 2014, Volume 10, Issue 2, Pages 61-69

Our aim in this paper is to solve some kinds of partial differential equations of the second order with variable coefficients, which have the general form
F_1 (x,y) Z_xx+F_2 (x,y) Z_xy+F_3 (x,y) Z_yy+F_4 (x,y) Z_x+F_5 (x,y) Z_y+F_6 (x,y)Z=0
such that F_1 (x,y),F_2 (x,y), F_3 (x,y), F_4 (x,y), F_5 (x,y) and F_6 (x,y)
are functions of xand y.By using the assumptionsZ(x,y)=e^(∫▒(U(x))/x dx+∫▒〖y^n V(y)dy〗) and
Z(x,y)=e^(∫▒〖U(x)〗 dx+∫▒V(y)dy) these assumptions will transform the second order partial differential equations to linear first order ordinary differential equation with two independent functions U(x) and V(y) .