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Domen
Domen
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Please help me solve the following equation using Solving DE with shooting method:

NDSolve[{(
    2 \[Pi] \[Epsilon] Cos[
    π ϵ 2Cos[2 \[Pi]π x] Sech[\[Kappa]Sech[κ + \[Epsilon] \[Kappa] Sin[
       ϵ κ 2Sin[2 \[Pi]π x]]^2 (2 \[Kappa]κ + 
       2 \[Epsilon]ϵ \[Kappa]κ Sin[2 \[Pi]π x] - 
         Sinh[2 \[Kappa]κ (1 + \[Epsilon] Sin[
            ϵ 2Sin[2 \[Pi]π x])]))/(\[Kappa]κ (1 + \[Epsilon] Sin[
        ϵ 2Sin[2 \[Pi]π x])^2) + 
    4 \[Pi] \[Epsilon] Cos[
   4 π ϵ 2Cos[2 \[Pi]π x] (1 + \[Epsilon]ϵ Sin[2 \[Pi]π x])^2 Derivative[1][p][Derivative[1][p][x] + 
      x] +  2/3 (1 + \[Epsilon]ϵ Sin[2 \[Pi]π x])^3 (p^\[Prime]\[Prime]p'')[
      x][x] == 0, 
  p[0] == 0, p[1] == 0}, p, x, 
  Method -> {"Shooting", 
   "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]

On running this code, the error getting displayed is:NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

Please help me solve the following equation using shooting method:

NDSolve[{(
    2 \[Pi] \[Epsilon] Cos[
      2 \[Pi] x] Sech[\[Kappa] + \[Epsilon] \[Kappa] Sin[
         2 \[Pi] x]]^2 (2 \[Kappa] + 
       2 \[Epsilon] \[Kappa] Sin[2 \[Pi] x] - 
       Sinh[2 \[Kappa] (1 + \[Epsilon] Sin[
             2 \[Pi] x])]))/(\[Kappa] (1 + \[Epsilon] Sin[
         2 \[Pi] x])^2) + 
    4 \[Pi] \[Epsilon] Cos[
      2 \[Pi] x] (1 + \[Epsilon] Sin[2 \[Pi] x])^2 Derivative[1][p][
      x] + 2/3 (1 + \[Epsilon] Sin[2 \[Pi] x])^3 (p^\[Prime]\[Prime])[
      x] == 0, p[0] == 0, p[1] == 0}, p, x, 
 Method -> {"Shooting", 
   "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]

On running this code the error getting displayed is:NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

Solving DE with shooting method

NDSolve[{(2 π ϵ Cos[2 π x] Sech[κ + ϵ κ Sin[2 π x]]^2 (2 κ + 2 ϵ κ Sin[2 π x] - 
         Sinh[2 κ (1 + ϵ Sin[2 π x])]))/(κ (1 + ϵ Sin[2 π x])^2) + 
         4 π ϵ Cos[2 π x] (1 + ϵ Sin[2 π x])^2 Derivative[1][p][x] + 
         2/3 (1 + ϵ Sin[2 π x])^3 (p'')[x] == 0, 
  p[0] == 0, p[1] == 0}, p, x, 
  Method -> {"Shooting", "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]

On running this code, the error getting displayed is

NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

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Trueee
Trueee
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Please help me solve the following equation using shooting method:

NDSolve[{(
    2 \[Pi] \[Epsilon] Cos[
      2 \[Pi] x] Sech[\[Kappa] + \[Epsilon] \[Kappa] Sin[
         2 \[Pi] x]]^2 (2 \[Kappa] + 
       2 \[Epsilon] \[Kappa] Sin[2 \[Pi] x] - 
       Sinh[2 \[Kappa] (1 + \[Epsilon] Sin[
             2 \[Pi] x])]))/(\[Kappa] (1 + \[Epsilon] Sin[
         2 \[Pi] x])^2) + 
    4 \[Pi] \[Epsilon] Cos[
      2 \[Pi] x] (1 + \[Epsilon] Sin[2 \[Pi] x])^2 Derivative[1][p][
      x] + 2/3 (1 + \[Epsilon] Sin[2 \[Pi] x])^3 (p^\[Prime]\[Prime])[
      x] == 0, p[0] == 0, p[1] == 0}, p, x, 
 Method -> {"Shooting", 
   "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]

On running this code the error getting displayed is:NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.