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**:**Re: DSolve and matrix form of system of equations***From:*Chris Chiasson <chris.chiasson@gmail.com>

**Re: DSolve and matrix form of system of equations***From:*Pratik Desai <pdesai1@umbc.edu>

**Re: DSolve and matrix form of system of equations***From:*Chris Chiasson <chris.chiasson@gmail.com>