Thanks Doctor

As i realized from your answer i have to put  _C2 = 0  to get a good result when r approach to zero. but i haven't know how to calculate _C1. because i don't know how sqrt(-_c[1])*r can be a zero of BesselJ(0,r) as r is variable.I mean how should i calculate the zero when r is variable and also we want to calculate _C1.

To calculate _C3 and _C4 we just need to put the boundary conditions in the equation?

and also i need to plot the equation. does Maple plot these kind of equations?

Thanks Doctor

As i realized from your answer i have to put  _C2 = 0  to get a good result when r approach to zero. but i haven't know how to calculate _C1. because i don't know how sqrt(-_c[1])*r can be a zero of BesselJ(0,r) as r is variable.I mean how should i calculate the zero when r is variable and also we want to calculate _C1.

To calculate _C3 and _C4 we just need to put the boundary conditions in the equation?

and also i need to plot the equation. does Maple plot these kind of equations?

I read that and tried to solve the problem but it has error. 

my boundary conditions was like below:

p(R, L) = pmo, P(-R, L) = P(R, L)=Pmo, P(r, 0) = pt, P(r, 1) = pmo    where pmo and pt are constants.

I wrote in Maple 11 :

d := [eta*(diff(p(r, L), `$`(L, 2))+(diff(r*(diff(p(r, L), r)), r))/r)+R*(diff(p(r, L), L)) = 0, p(R, L) = pmo, P(-R, L) = P(R, L), P(r, 0) = pt, P(r, 1) = pmo]

> pdsolve(d, build);

%;Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [p(r,L), p(R,L)], [P(R,L), P(-R,L)], [P(-R,L), P(r,0)], [P(r,0), P(r,1)]

it gave me this error. how can i solve it?

I read that and tried to solve the problem but it has error. 

my boundary conditions was like below:

p(R, L) = pmo, P(-R, L) = P(R, L)=Pmo, P(r, 0) = pt, P(r, 1) = pmo    where pmo and pt are constants.

I wrote in Maple 11 :

d := [eta*(diff(p(r, L), `$`(L, 2))+(diff(r*(diff(p(r, L), r)), r))/r)+R*(diff(p(r, L), L)) = 0, p(R, L) = pmo, P(-R, L) = P(R, L), P(r, 0) = pt, P(r, 1) = pmo]

> pdsolve(d, build);

%;Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [p(r,L), p(R,L)], [P(R,L), P(-R,L)], [P(-R,L), P(r,0)], [P(r,0), P(r,1)]

it gave me this error. how can i solve it?

Thanks alot Oliver. I got the answer but i have some quetions about the answer.

1- it seems that it is a analytical solution of the equation. does Maple do it numerically? 

2- How can i find that coefficients like C1 and C2 in the answer? because my purpose is to change eta and plot P Vs. eta in different situations.

( I mean my boundary conditions are like below. how can i apply them to the equation)

I'm sorry, i am new in Maple and i don't know much.

Thanks alot Oliver. I got the answer but i have some quetions about the answer.

1- it seems that it is a analytical solution of the equation. does Maple do it numerically? 

2- How can i find that coefficients like C1 and C2 in the answer? because my purpose is to change eta and plot P Vs. eta in different situations.

( I mean my boundary conditions are like below. how can i apply them to the equation)

I'm sorry, i am new in Maple and i don't know much.

Thanks Oliver, but are you sure that this part "1/r*diff(r*p(r,L),r))" of your answer is correct? because it is a second order but you write it as a first order.

Thanks Oliver, but are you sure that this part "1/r*diff(r*p(r,L),r))" of your answer is correct? because it is a second order but you write it as a first order.