I'm trying to solve a differential equation which solution is in the form of Bessel functions. One of the boundary conditions is at infinity. I use:
ψ[R_] = ψ[R] /. DSolve[{ψ''[R] + (ψ'[R])/R - κ^2 ψ[R] == 0,
ψ[a/2] == Psi0, ψ[M] == 0}, ψ[R], R][[1]]
Limit[ψ[R], M -> Infinity]
Simplify[%, {r > 0 && κ > 0 && a > 0 && Psi0 ∈ Reals}]
And obtain:
How can I obtain the solution of my problem overpassing the time limit?
\[Psi][R] =(Psi0 BesselK[0, k R])/BesselK[0, (a k)/2]
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