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MathGroup Archive 2005

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DSolve and matrix form of system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61294] DSolve and matrix form of system of equations
  • From: "Matt" <anonmous69 at netscape.net>
  • Date: Fri, 14 Oct 2005 05:56:15 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,
  I've been generally taking the 2 dimensional systems of differential
equations that I've been working with and typing them out explicitly
(e.g. x'[t] == x[t] + 2 y[t], y'[t] == -2 x[t] + y[t]), but tonight I
decided to enter them into Mathematica in the matrix form:

Cell[BoxData[
    RowBox[{
      RowBox[{"eqn", " ", "=", " ",
        RowBox[{
          RowBox[{"(", GridBox[{
                {
                  RowBox[{
                    RowBox[{"x", "'"}], "[", "t", "]"}]},
                {
                  RowBox[{
                    RowBox[{"y", "'"}], "[", "t", "]"}]}
                }], ")"}], "\[Equal]",
          RowBox[{
            RowBox[{"(", GridBox[{
                  {"a",
                    RowBox[{
                      SqrtBox["2"], " ", "+", " ",
                      RowBox[{"a", "/", "2"}]}]},
                  {
                    RowBox[{
                      SqrtBox["2"], " ", "-", " ",
                      RowBox[{"a", "/", "2"}]}], "0"}
                  }], ")"}], ".",
            RowBox[{"(", GridBox[{
                  {
                    RowBox[{"x", "[", "t", "]"}]},
                  {
                    RowBox[{"y", "[", "t", "]"}]}
                  }], ")"}]}]}]}], ";"}]], "Input"]

and I was wondering what would be the preferred/efficient method of
getting the actual equations back out of the expression denoted by
'eqn' above?

What I did was this:

Cell[BoxData[
    RowBox[{"sols", " ", "=", " ",
      RowBox[{"Table", "[",
        RowBox[{
          RowBox[{"DSolve", "[",
            RowBox[{
              RowBox[{"{",
                RowBox[{
                  RowBox[{
                    RowBox[{
                      RowBox[{"eqn", "[",
                        RowBox[{"[",
                          RowBox[{"1", ",", "1"}], "]"}], "]"}], "[",

                      RowBox[{"[", "1", "]"}], "]"}], " ", "\[Equal]",
                     " ",
                    RowBox[{
                      RowBox[{"eqn", "[",
                        RowBox[{"[",
                          RowBox[{"2", ",", "1"}], "]"}], "]"}], "[",

                      RowBox[{"[", "1", "]"}], "]"}]}], ",",
                  RowBox[{
                    RowBox[{
                      RowBox[{"eqn", "[",
                        RowBox[{"[",
                          RowBox[{"1", ",", "2"}], "]"}], "]"}], "[",

                      RowBox[{"[", "1", "]"}], "]"}], " ", "\[Equal]",
                     " ",
                    RowBox[{
                      RowBox[{"eqn", "[",
                        RowBox[{"[",
                          RowBox[{"2", ",", "2"}], "]"}], "]"}], "[",

                      RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], ",",
              " ",
              RowBox[{"{",
                RowBox[{
                  RowBox[{"x", "[", "t", "]"}], ",",
                  RowBox[{"y", "[", "t", "]"}]}], "}"}], ",", "t"}],
            "]"}], ",",
          RowBox[{"{",
            RowBox[{"a", ",",
              RowBox[{"-", "2"}], ",", "2"}], "}"}]}],
        "]"}]}]], "Input"]

which worked for me, but again, I'm sure there's a better or more
elegant Mathematica way to get the equations back out of 'eqn'.

Thanks for any insight,

Matt


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