I'm experiencing troubles in obtaining the result of an ordinary differential equation with a boundary condition at infinity.
I write down

    Limit[DSolve[{\[Psi]''[r] + 2/r*\[Psi]'[r] - \[Kappa]^2*\[Psi][r] == 
        0, \[Psi][a/2] == Subscript[Psi, 0], \[Psi][M] == 0}, \[Psi][r], 
      r], M -> Infinity]

And obtain 

    \!\(\*UnderscriptBox[\(\[Limit]\), \(M \[Rule] \[Infinity]\)]\) {{\
    \[Psi][r] -> (
        a E^((a \[Kappa])/2 - 
          r \[Kappa]) (-E^(2 M \[Kappa]) + E^(2 r \[Kappa])) Subscript[
         Psi, 0])/(2 (E^(a \[Kappa]) - E^(2 M \[Kappa])) r)}}

Which is correct, but is not evaluated for the limit.
How can I force Mathematica to evaluate this limit?