Question: Steady state for an ODE with diffusion term

Hi there,

I am currently working on an ODE model with a diffusion term and I have to analyse it analytically (if possible) with Maple12.

With the dsolve function I have a solution but based on BesselJ and BesselY functions.

My questions are:

• Do you know if it's possible to have a solution without these functions?
• When I add the IBCs conditions, the system is inconsistent, do you understand why?

Any ideas?

Thank you very much for your help!

My worksheet is:

> eq1 := Dif *( diff(c(r),(r$2)) + (diff(c(r),r)/r) )-rho*c(r)+alpha=0; # with Dif the diffusion, rho the degradation and alpha the production terms. c(r) is the concentratoin of c at the distance r

> BC1 := (D[1](c))(0) = 0;   # boundary condition : symmetry about the center r = 0

> BC2 := (D[1](c))(R[2]) = 0;   # boundary condition : it's not possible to diffuse after R[2]

> IC := c(r) = 0;   # initial condition

> sol1[1] := rhs(dsolve(eq1, c(r)));

> sol1[2] := dsolve({BC1, BC2, IC, eq1}, c(r));

Warning, system is inconsistent.

Thank you in advance!