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
- Follow-Ups:
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- Re: DSolve and matrix form of system of equations
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