Dear my friends

Hi

I have a linear partial differential equation to solve.

> equ1:=F5*(diff(phi(r, theta), r, r)+(diff(phi(r, theta), r))/r+(diff(phi(r, theta), theta, theta))/r^2)+F3*phi(r,theta) = 0;

where F5 and F3 is constant and phi(r,theta) is unknown function.

I tried to solve this equation by the following Maple's command:

> pdsolve(equ1,phi(r,theta));

The result is obtained by:

phi(r,theta) = -Intat(Intat(F3*phi(_a,-I*ln(_a)+2*I*ln(_b)-I*ln(r)+theta)/F5*_a,_a = _b)/_b,_b = r)+_F1(I*ln(r)+theta)+_F2(-I*ln(r)+theta)

In the first view, it is obvious that the result of above command is an expression containing imaginary symbol (I). This means that  phi(r, theta) is a complex expression; even though, existing complex number in phi(r,theta) does not have any physical concept. In fact, this PDE raised from a mechanical problem which dose not have any relationship with imaginary numbers and works in real domain.

It is worth mentioning that phi(r,theta) is to obtain by solving the following partial differential equation:

> equ2:=F2*(diff(phi(r, theta), r, r)+(diff(phi(r, theta), r))/r+(diff(phi(r, theta), theta, theta))/r^2)+F3*phi(r, theta) = 0;

by using the following command, phi(r,theta) can be obtained:

> pdsolve(equ2,phi(r,theta),build);
The result of above is obtained by:

phi(r,theta)= _C1*BesselJ((_c/F2)^(1/2),(F3/F2)^(1/2)*r)*_C3*sin(1/F2^(1/2)*_c^(1/2)*theta)+_C1*BesselJ((_c/F2)^(1/2),(F3/F2)^(1/2)*r)*_C4*cos(1/F2^(1/2)*_c^(1/2)*theta)+_C2*BesselY((_c/F2)^(1/2),(F3/F2)^(1/2)*r)*_C3*sin(1/F2^(1/2)*_c^(1/2)*theta)+_C2*BesselY((_c/F2)^(1/2),(F3/F2)^(1/2)*r)*_C4*cos(1/F2^(1/2)*_c^(1/2)*theta);

I used the above relation of phi(r,theta) to solve equ1. However, the results is again dependence on complex number which is not acceptable for my work. 