# [pstricks] ODEs

Fri Feb 6 19:25:27 CET 2009

All,

Well I gave up and used Matlab to compute the initial conditions
needed at t=-2. Still, only 2 of my 4 solution trajectories are
plotting.

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\documentclass{article}
\usepackage{amsmath}

\begin{document}

\def\Funct{dup 3 exp exch sub}
\psset{unit=2cm,arrowscale=2}
\begin{center}
\begin{pspicture}(-2,-2)(2,2)
\psaxes[labels=none,ticksize=0 0pt]{<->}(0,0)(-2,-2)(2,2)[$t$,0][$y$,0]
\psline[linecolor=blue,linewidth=1pt]{<->}(-2,-1)(2,-1)
\psline[linecolor=blue,linewidth=1pt]{<->}(-2,0)(2,0)
\psline[linecolor=blue,linewidth=1pt]{<->}(-2,1)(2,1)
\psplotDiffEqn[linecolor=black,method=varrkiv,varsteptol=0.0001]{-2}
{2}{-1.0051}{\Funct}
\psplotDiffEqn[linecolor=black,method=varrkiv,varsteptol=0.0001]{-2}
{2}{-0.9736}{\Funct}
\psplotDiffEqn[linecolor=black,method=varrkiv,varsteptol=0.0001]{-2}
{2}{0.9736}{\Funct}
\psplotDiffEqn[linecolor=black,method=varrkiv,varsteptol=0.0001]{-2}
{2}{1.0051}{\Funct}
\uput[l](-2,1){$y=1$}
\uput[l](-2,0){$y=0$}
\uput[l](-2,-1){$y=-1$}
\pscircle[fillstyle=solid,fillcolor=white,linecolor=blue](0,1){3pt}
\pscircle[fillstyle=solid,fillcolor=blue,linecolor=blue](0,0){3pt}
\pscircle[fillstyle=solid,fillcolor=white,linecolor=blue](0,-1){3pt}
\psset{arrowscale=1}
\psline[linecolor=red,linewidth=3pt]{->}(0,1.3)(0,1.7)
\psline[linecolor=red,linewidth=3pt]{<-}(0,0.3)(0,0.7)
\psline[linecolor=red,linewidth=3pt]{->}(0,-0.7)(0,-0.3)
\psline[linecolor=red,linewidth=3pt]{->}(0,-1.3)(0,-1.7)
\end{pspicture}
\end{center}

\end{document}

Any help appreciated.

David.