Problem with InverseFunction
- To: mathgroup at smc.vnet.net
- Subject: [mg28199] Problem with InverseFunction
- From: Low Choon Song <eng81288 at nus.edu.sg>
- Date: Wed, 4 Apr 2001 04:13:22 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello, I have this problem that I have been trying to solve for weeks now. But I still can't succeed. I use DSolve in Mathematica to solve a Differential Eqn and in the output by Mathematica, it always come out with the form of InverseFunction. How can I express the results( output ) in a more readable form? How can I get rid of the InverseFunction? How can I get rid of the "#1" that appear in the solution? The problem I am solving is below and I have attached it too, if you are willing to take a quick look. Thanks in advance. Low (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. 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\ \(\(1\ \)\(\ \)\)\/\(\(4\)\(\ \)\)\ \((k\/d)\)\ \((P\/\(Rg\ T\))\)\ \((R[ t]\ )\))\), \ R[0] \[Equal] \ 0}, \ R[t], \ t}, \ InverseFunctions\ \[Rule] \ False]\)}], "Input"], Cell[BoxData[ \(DSolve::"argct" \(\(:\)\(\ \)\) "\!\(DSolve\) called with \!\(2\) arguments."\)], "Message"], Cell[BoxData[ RowBox[{"DSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(Rg\ T\ \((\(-2\)\ k + \@\(k\^2\/4 + \(2\ C\ \[Infinity]\ d\ k\ Rg\ T\)\/\(P\ R[t]\)\))\)\ \((\(-\(\(k\ P\ R[ t]\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\ \[Infinity]\ k\ P\ R[t]\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ R[t]\^2\)\/\(16\ d\ \^2\ Rg\^2\ T\^2\)\))\)\)\/P\)}], ",", \(R[0] == 0\)}], "}"}], ",", \(R[t]\), ",", "t"}], "}"}], ",", \(InverseFunctions \[Rule] False\)}], "]"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(Rg\ T\ \((\(-2\)\ k + \@\(k\^2\/4 + \(2\ C\[Infinity]\ \ d\ k\ Rg\ T\)\/\(P\ R[t]\)\))\)\ \((\(-\(\(k\ P\ R[ t]\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\ \[Infinity]\ k\ P\ R[t]\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ R[t]\^2\)\/\( 16\ d\ \^2\ Rg\^2\ T\^2\)\))\)\)\/P\)}], ",", \(R[0] == 0\)}], "}"}], ",", \(R[t]\), ",", "t"}], "]"}]], "Input"], Cell[BoxData[ \({R[t] \[Rule] \(InverseFunction[ C[1] - \((32\ d\ Log[ 8\ C\[Infinity]\ d\ Rg\ T - 15\ k\ P\ #1]\ \@\(\(8\ C\[Infinity]\ d\ k\ Rg\ T + \ k\^2\ P\ #1\)\/\(P\ #1\)\)\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ \ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\)\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 \ + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\))\)/\((225\ k\^3\ \((8\ C\ \[Infinity]\ d\ Rg\ T + k\ P\ #1)\)\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ \ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ \ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\))\) + \(1\/\(Rg\ T\)\) \((P\ \ \((\(-\(\(8\ Log[\(-8\)\ C\[Infinity]\ d\ Rg\ T + 15\ k\ P\ #1]\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ \ P\ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\)\)\/\(225\ k\^2\ \ P\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\ \)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\)\)\ \)\) - \(17\ Log[2\ \((4\ C\[Infinity]\ d\ Rg\ T + k\ P\ #1)\) + 2\ P\ #1\ \@\ \(\(8\ C\[Infinity]\ d\ k\ Rg\ T + k\^2\ P\ #1\)\/\(P\ #1\)\)]\ \((\(-k\)\ P\ \ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ P\^2\ \ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\)\)\/\(225\ k\^2\ P\ \((\(-\(\(k\ P\ #1\)\/\ \(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\/\(2\ d\ Rg\ T\) + \ \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\)\) + \((8\ \ Log[\(-\(\(3375\ k\^2\ P\^2\ #1\ \@\(\(8\ C\[Infinity]\ d\ k\ Rg\ T + k\^2\ P\ \ #1\)\/\(P\ #1\)\)\)\/\(128\ C\[Infinity]\ d\ Rg\ T\ \((\(-8\)\ C\[Infinity]\ \ d\ Rg\ T + 15\ k\ P\ #1)\)\)\)\) + \(3375\ \((8\ \ C\[Infinity]\ d\ k\^2\ P\ Rg\ T + 17\ k\^3\ P\^2\ #1)\)\)\/\(1024\ C\ \[Infinity]\ d\ Rg\ T\ \((8\ C\[Infinity]\ d\ Rg\ T - 15\ k\ P\ #1)\)\)]\ \((\ \(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ \ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\))\)/\((225\ k\^2\ \ P\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\ \/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\))\) \ - \((68\ Log[2\ \((4\ C\[Infinity]\ d\ Rg\ T + k\ P\ #1)\) + 2\ d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ \ P\ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\)]\ \((\(-k\)\ P\ \ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ P\^2\ \ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\))\)/\((225\ k\^2\ P\ \((\(-\(\(k\ P\ \ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\/\(2\ d\ Rg\ T\) + \ \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\))\) + \((32\ Log[\(3375\ \ \((8\ C\[Infinity]\ d\ k\^2\ P\ Rg\ T + 17\ k\^3\ P\^2\ #1)\)\)\/\(4096\ C\ \[Infinity]\ d\ Rg\ T\ \((8\ C\[Infinity]\ d\ Rg\ T - 15\ k\ P\ #1)\)\) - \ \(3375\ k\^2\ P\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ P\^2\ \ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\)\)\/\(512\ C\[Infinity]\ \((\(-8\)\ C\ \[Infinity]\ d\ Rg\ T + 15\ k\ P\ #1)\)\)]\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ \ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\))\)/\((225\ k\^2\ \ P\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\ \/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\))\) \ - \(#1\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ \ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\)\)\/\(15\ C\[Infinity]\ d\ \ k\ Rg\ T\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ \ P\ #1\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\ \))\)\) - \(#1\ \@\(\(8\ C\[Infinity]\ d\ k\ Rg\ T + k\^2\ P\ #1\)\/\(P\ #1\)\ \)\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + \ k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\)\)\/\(60\ C\[Infinity]\ d\ \ k\^2\ Rg\ T\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ \ k\ P\ #1\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ \ T\^2\)\))\)\) - \(\@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ P\^2\ \ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\)\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\ \[Infinity]\ d\ k\ P\ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ \ T\^2\)\))\)\)\/\(15\ C\[Infinity]\ k\^2\ P\ \((\(-\(\(k\ P\ #1\)\/\(4\ d\ Rg\ \ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\/\(2\ d\ Rg\ T\) + \(k\^2\ P\^2\ \ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\)\) + \((\@\(\(8\ C\[Infinity]\ d\ k\ \ Rg\ T + k\^2\ P\ #1\)\/\(P\ #1\)\)\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ Rg\ T\ #1 \ + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\)\ \((\(-\(1\/\(60\ C\[Infinity]\ \ k\^3\ P\)\)\) + \(2\ d\ Rg\ T\)\/\(15\ k\^3\ P\ \((8\ C\[Infinity]\ d\ Rg\ \ T + k\ P\ #1)\)\))\)\ \((\(-k\)\ P\ #1 + d\ Rg\ T\ \@\(\(8\ C\[Infinity]\ d\ k\ P\ \ Rg\ T\ #1 + k\^2\ P\^2\ #1\^2\)\/\(d\^2\ Rg\^2\ T\^2\)\))\))\)/\((\(-\(\(k\ P\ \ #1\)\/\(4\ d\ Rg\ T\)\)\) + \@\(\(C\[Infinity]\ k\ P\ #1\)\/\(2\ d\ Rg\ T\) \ + \(k\^2\ P\^2\ #1\^2\)\/\(16\ d\^2\ Rg\^2\ T\^2\)\))\))\))\) &]\)[ t]}\)], "Output"] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 800}, {0, 527}}, WindowSize->{792, 500}, WindowMargins->{{-3, Automatic}, {Automatic, -1}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic} ] (*********************************************************************** Cached data follows. 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