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Liebe Mathematica-Gemeinde, mit DSolve habe ich die Loesung einer Differentialgleichung gefunden, allerdings ist der Ausdruck mit den vorkommenden Konstanten ziemlich lange. Ich weiss aber dass erdie folgende Form haben muss: f[x] = C[1] + k1 C[2] Exp[a1 x] + k2 C[3] Exp[a2 x] Die Konstanten k1,k2,a1 und a2 sind zu bestimmen. Ein Versuch mit Solve scheitert an der Exp Funktion, ueberhaupt scheint der Ausdrucke kein Polynom in C[] zu sein. Kann mir jemand eine Anregung geben, wie ich Mathematica zu einem Koeffizientenvergleich veranlasse ? Mit freundlichen Gruessen, Rudolf Schuch schuch@XXXXXXX.de (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@XXXXXXX.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 41594, 744]*) (*NotebookOutlinePosition[ 42229, 767]*) (* CellTagsIndexPosition[ 42185, 763]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(gensol\ = \ DSolve[\ { wwh\ \(Th'\)[x]\ == \ k\ A\ \((Tk[x]\ - Th[x])\)\ - \ lambda\ \(\(Th'\)'\)[x], \n \t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ wwk\ \(Tk'\)[x]\ == \ k\ A\ \((\ Tk\ [x] - \ Th[x])\)\ }, \ {\ Th[x], Tk[x]}, \ x]\)], "Input"], Cell[BoxData[ \({{Th[x] \[Rule] C[1] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) + \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) - \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[2] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) - \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[3], Tk[x] \[Rule] C[1] + \(( \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) - \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[2] + \(( \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[3]}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[\ Th[x]\ == \ C[1]\ + \ lkh1\ C[2]\ Exp[e1\ x]\ + \ lkh2\ C[3]\ Exp[e2\ x], \ {\ lkh1, lkh2, \ e1, e2\ }] /. \ gensol\)], "Input"], Cell[BoxData[ \(Solve::"tdep" \( : \ \) "The equations appear to involve transcendental functions of the \ variables in an essentially non-algebraic way."\)], "Message"], Cell[BoxData[ \(Solve::"svars" \( : \ \) "Equations may not give solutions for all \"solve\" variables."\)], "Message"], Cell[BoxData[ \(Solve::"tdep" \( : \ \) "The equations appear to involve transcendental functions of the \ variables in an essentially non-algebraic way."\)], "Message"], Cell[BoxData[ \(Solve::"svars" \( : \ \) "Equations may not give solutions for all \"solve\" variables."\)], "Message"], Cell[BoxData[ \({Solve[ C[1] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) + \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) - \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[2] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) - \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\)\) + \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[3] == C[1] + E\^\(e1\ x\)\ lkh1\ C[2] + E\^\(e2\ x\)\ lkh2\ C[3], {lkh1, lkh2, e1, e2}]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Second[Th[x]]\ /. \ gensol\)], "Input"], Cell[BoxData[ \({Second[ C[1] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) + \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2\ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2\ lambda\^2\ wwk\))\)\) - \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\))\))\)\ C[2] + \((\(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) - \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2\ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2\ lambda\^2\ wwk\))\)\) + \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2 \ lambda\^2\ wwk\))\))\))\)\ C[3]]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(PolynomialQ[Th[x], {C[1], C[2], C[3]}] /. gensol\)], "Input"], Cell[BoxData[ \({True}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(thsol\ = \ Solve[Th[x]\ == \ C[1] + lkh1\ fh1[x]\ C[2]\ + \ lkh2\ fh2[x]\ C3, \ {lkh1, lkh2\ , fh1[x], \ fh2[x]}]\ /. \ gensol\)], "Input"], Cell[BoxData[ \(Solve::"svars" \( : \ \) "Equations may not give solutions for all \"solve\" variables."\)], "Message"], Cell[BoxData[ \({{{lkh1 \[Rule] \(1\/\(C[2]\ fh1[x]\)\(( \((\(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) + \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\)\) - \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk - \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) - \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[2] + \(( \(-\(\(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ wwh \)\/\(2\ A\ k\)\)\) - \(E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\ wwk\) - \(1\/\(2\ A\ k\ wwk\)\(( E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk) \) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)) \)\) + \(A\^2\ E \^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\)\) + \(A\ E\^\(\(\(( A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ wwh\)\/\(2\ lambda\ wwk\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\)\) + \((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk + \@\(\(-4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \))\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)/ \((2\ lambda\ wwk\^2\ \(( \(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) + \(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) + \(A\ k\ \@\(\( - 4\)\ A\ k\ lambda\ wwk\ \(( \(-wwh\) + wwk)\) + \((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2 \)\)\/\(2\ lambda\^2\ wwk\))\))\))\)\ C[3] - C3\ lkh2\ fh2[x])\)\)}}}\)], "Output"] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1152}, {0, 900}}, WindowSize->{902, 602}, WindowMargins->{{Automatic, 31}, {31, Automatic}} ] (*********************************************************************** Cached data follows. 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