(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[      4536,        134]
NotebookOptionsPosition[      3850,        113]
NotebookOutlinePosition[      4363,        131]
CellTagsIndexPosition[      4320,        128]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"v", "[", "x_", "]"}], " ", "=", " ", 
   RowBox[{"2", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Sin", "[", "x", "]"}], "^", "4"}], " ", "-", " ", "1"}], 
     ")"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.4830067148839893`*^9, 3.483006726020898*^9}, {
   3.483006779375214*^9, 3.4830068222211103`*^9}, {3.483006991765932*^9, 
   3.483007021360951*^9}, 3.483007208497789*^9, {3.561057611071662*^9, 
   3.561057623235271*^9}, {3.5610576628888807`*^9, 3.561057663148275*^9}, {
   3.561057761164893*^9, 3.56105776555626*^9}, {3.561057799123131*^9, 
   3.561057814487924*^9}, {3.561057878387388*^9, 3.5610578786106253`*^9}, {
   3.561058145716416*^9, 3.561058147971891*^9}, 3.5610585027478943`*^9, {
   3.735649586773919*^9, 3.73564964719483*^9}, {3.7356496969219837`*^9, 
   3.7356496980010567`*^9}, 
   3.735650639872857*^9},ExpressionUUID->"860f3665-231d-41a6-9daf-\
5670eda9236b"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"xmax", " ", "=", " ", "40.0"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"v", "[", "x", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "xmax"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.7356504994995527`*^9, 
  3.7356505247477417`*^9}},ExpressionUUID->"581350e7-a4fd-4b35-8165-\
a4aaf02bdcdb"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"eig", " ", "=", " ", 
    RowBox[{"-", "1.4"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sol", " ", "=", 
   RowBox[{"NDSolve", "[", 
    RowBox[{
     RowBox[{"{", " ", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "/", "2"}], ")"}], " ", 
          RowBox[{
           RowBox[{"y", "''"}], "[", "x", "]"}]}], "+", 
         RowBox[{
          RowBox[{"v", "[", "x", "]"}], " ", 
          RowBox[{"y", "[", "x", "]"}]}]}], "\[Equal]", 
        RowBox[{"eig", " ", 
         RowBox[{"y", "[", "x", "]"}]}]}], ",", 
       RowBox[{
        RowBox[{"y", "[", "0", "]"}], "\[Equal]", "1"}], ",", 
       RowBox[{
        RowBox[{
         RowBox[{"y", "'"}], "[", "0", "]"}], "\[Equal]", "0"}]}], "}"}], ",",
      "y", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "xmax"}], "}"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"eig", "+", 
      RowBox[{"Evaluate", "[", 
       RowBox[{
        RowBox[{"y", "[", "x", "]"}], "/.", "  ", "sol"}], "]"}]}], ",", 
     "eig", ",", 
     RowBox[{"v", "[", "x", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "xmax"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "3"}], ",", "3"}], "}"}]}]}], "]"}], "\n"}], "Input",
 CellChangeTimes->CompressedData["
1:eJxTTMoPSmViYGAQAWIQfWqDzXu/zy8dDSb/+Ayim2Qjmf2B9JuO52C6gi+N
A0Sbqf4E01OCtHhBtE+ROx+IZsp/IA2id12wkwHRfidblUD0rH2HdUC0db2l
IYi+tTPbCkS3vjnxskHoleObOJ/XIHpZytZPIHpz9aRvILpH+cBq3Y5XjtsY
uNaA6P2FvZtANJPkm50gOq503xEQvetz1HEQPeXglosg+oK12DUQrZPn9BZE
S7R2vAPRGt1mUnpAumGroyqI7p7lagCib1x/BqZPP09Yr3/1teNO7ikbQfSV
TrltIFrg1JwTIHp7UKGsAZAOX+yvAaL3pG7QBdFn/HeCaQD5GKYN
  
  "],ExpressionUUID->"6354f0e4-9fe2-422d-bea7-a0ac079d553a"]
},
WindowSize->{919, 885},
WindowMargins->{{484, Automatic}, {Automatic, 23}},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
Magnification:>FEPrivate`If[
  FEPrivate`Equal[FEPrivate`$VersionNumber, 6.], 1.5, 1.5 Inherited],
FrontEndVersion->"11.1 for Linux x86 (64-bit) (April 18, 2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 952, 20, 51, "Input", "ExpressionUUID" -> \
"860f3665-231d-41a6-9daf-5670eda9236b"],
Cell[1500, 42, 387, 10, 83, "Input", "ExpressionUUID" -> \
"581350e7-a4fd-4b35-8165-a4aaf02bdcdb"],
Cell[1890, 54, 1956, 57, 248, "Input", "ExpressionUUID" -> \
"6354f0e4-9fe2-422d-bea7-a0ac079d553a"]
}
]
*)