# How to force Mathematica to evaluate a limit in the boundary conditions of a differential equation?

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

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

And obtain

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

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