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MathGroup Archive 2005

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Re: DSolve and matrix form of system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61348] Re: [mg61294] DSolve and matrix form of system of equations
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Sun, 16 Oct 2005 00:18:02 -0400 (EDT)
  • References: <200510140956.FAA28648@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thinking about it a little further,

And@@Sequence@@@MapThread[Equal,List@@eqn,2]

or

MapThread[Equal,List@@eqn,2]/.List->And

would be more appropriate than my first response.

On 10/14/05, Matt <anonmous69 at netscape.net> wrote:
> 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
>
>


--
Chris Chiasson
http://chrischiasson.com/contact/chris_chiasson


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