(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 187186, 6171]*) (*NotebookOutlinePosition[ 188289, 6207]*) (* CellTagsIndexPosition[ 188245, 6203]*) (*WindowFrame->Normal*) Notebook[{ Cell["34 points", "Section", FormatType->TextForm], Cell[TextData[{ " ", StyleBox["Probl\[EGrave]me 1 ", Evaluatable->False, AspectRatioFixed->True, FontSize->12, FontWeight->"Bold"], StyleBox["(6 points)", Evaluatable->False, AspectRatioFixed->True, FontSize->9, FontWeight->"Plain"] }], "Subsubsection"], Cell[TextData[StyleBox["R\[EAcute]solvons l'\[EAcute]quation par rapport \ \[AGrave] y[x]:", Evaluatable->False, AspectRatioFixed->True]], "Text", FormatType->TextForm], Cell[CellGroupData[{ Cell["sol=DSolve[{y'[x]==Exp[-y[x]]Cos[Pi x]^2},y[x],x]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{y[x] \[Rule] Log[x\/2 + C[1] + Sin[2\ \[Pi]\ x]\/\(4\ \[Pi]\)]}}\)], "Output"] }, Open ]], Cell["Examinons la solution pour x=0", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["sol/.x->0", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{y[0] \[Rule] Log[C[1]]}}\)], "Output"] }, Open ]], Cell[TextData[{ "Sachant qu'en x=0 y=ln(e), nous en d\[EAcute]duisons que C[1] est \ \[EAcute]gal \[AGrave] e (rappel : dans ", StyleBox["Mathematica", FontSlant->"Italic"], ", la fonction Log[x] donne le logarithme naturel de x). 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