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
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\(gensol\ = \
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\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \
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\@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((
\(-wwh\) + wwk)\) +
\((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2
\ lambda\^2\ wwk\))\)\) +
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\(-wwh\) + wwk)\) +
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\(-wwh\) + wwk)\) +
\((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2
\ lambda\^2\ wwk\))\)\) +
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C[3]}}\)], "Output"]
}, Open ]],
Cell[CellGroupData[{
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\(Solve[\
Th[x]\ == \
C[1]\ + \ lkh1\ C[2]\ Exp[e1\ x]\ + \ lkh2\ C[3]\ Exp[e2\ x],
\ {\ lkh1, lkh2, \ e1, e2\ }] /. \ gensol\)], "Input"],
Cell[BoxData[
\(Solve::"tdep" \( : \ \)
"The equations appear to involve transcendental functions of the \
variables in an essentially non-algebraic way."\)], "Message"],
Cell[BoxData[
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"Equations may not give solutions for all \"solve\" variables."\)],
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\)\/\(2\ A\ k\)\)\) -
\(E\^\(\(\((A\ k\ lambda - wwh\ wwk -
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\)\ x\)\/\(2\ lambda\ wwk\)\)\ lambda\)\/\(2\
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\(1\/\(2\ A\ k\ wwk\)\((
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\)\ x\)\/\(2\ lambda\ wwk\)\)\
\@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((\(-wwh\) + wwk)\) +
\((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))\)\) +
\(A\^2\ E
\^\(\(\((
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\@\(\(-4\)\ A\ k\ lambda\ wwk\ \((
\(-wwh\) + wwk)\) +
\((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\))
\)\ x\)\/\(2\ lambda\ wwk\)\)\ k\^2\)\/\(2\
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\(-\(\(A\ k\ wwh\)\/\(2\ lambda\^2\)\)\) +
\(A\^2\ k\^2\)\/\(2\ lambda\ wwk\) -
\(A\ k\
\@\(\( - 4\)\ A\ k\ lambda\ wwk\ \((
\(-wwh\) + wwk)\) +
\((\(-A\)\ k\ lambda + wwh\ wwk)\)\^2\)\)\/\(2
\ lambda\^2\ wwk\))\)\) +
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\((A\ E\^\(\(\((A\ k\ lambda - wwh\ wwk -
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\(-wwh\) + 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"]
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