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edited Dec 22, 2018 at 8:08

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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]ψ''[r] + 2/r*\[Psi]'[r]r*ψ'[r] - \[Kappa]^2*\[Psi][r]κ^2*ψ[r] == 
    0, \[Psi][aψ[a/2] == Subscript[Psi, 0], \[Psi][M]ψ[M] == 0}, \[Psi][r]ψ[r], 
  r], M -> Infinity]

And obtain

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

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

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?

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?

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asked Dec 22, 2018 at 0:26

Adrián Silva Caballero

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[{\[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?

differential-equations boundary-conditions