Author : Hassan Mohammed, Ali
"Finding the complete solution of special types of the second order partial differential equations with variable coefficients"
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) .