% !TEX TS-program = latex
\documentclass[11pt]{amsart}
\usepackage{pstricks, pst-plot, pst-ode}
\usepackage{multido}


%\title{Brief Article}
%\author{The Author}
%%\date{}                                           % Activate to display a given date or no date

\begin{document}
%\maketitle
%\section{}
%\subsection{}


\def\tEnd{10} % end of integration interval; in- or de-crease to have longer/shorter lines
\def\outputSteps{500} %increase for smoother lines (and larger PDF file)


\pstVerb{
	/A 1 def
	/B -2 def
	/C 1 def
	/D -1 def
}

% Solve linear o.d.e.x'=Ax+By,  y'=Cx+Dy
\multido{\ii=0+1,\rx=-5.0+0.5}{20}{
	\multido{\ij=0+1,\ry=-5.0+0.5}{20}{
                    \pstODEsolve[algebraicAll]{line_\ii_\ij}{x[0] | x[1]}{0}{\tEnd}{\outputSteps}{\rx | \ry}{%
                    	A*x[0]+B*x[1] |
                    	C*x[0]+D*x[1]
                    	}
	}
}

\begin{pspicture}(-5.5,-5.5)(5.5,5.5)

\psclip{\psframe(-5.0,-5.0)(5.0,5.0)}%

  %plot the lines previously computed
  \multido{\ii=0+1}{20}{
    \multido{\ij=0+1}{20}{
      \listplot{line_\ii_\ij}
	}
}
\end{pspicture}
\end{document}