Numerical Solution for Bessel Equation

Hello folks,

I'm trying to solve the Bessel equation that arises from the heat transfer equation of a straight triangulat fin. I know the analytical solution, but need to calculate the numerical solution for comparison purposes.

At the tip of the fin we know that dT/dx=0 and that at the base T(x)=Tb. I've tried using odesolve but it cannot solve the equation, so I'm thinking that odesolve is not the right solver, but do not know which one I should use. In this case, I placed the origin at the tip of the fin to simplify the differential equation.

Please take a look at the attached file for additional details

Any suggestions or recommendations would be greatly appreciated.

Thanks!