\documentclass{article}
\usepackage{pst-ode,pst-plot}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}%

\begin{document}
\begin{center}
\psset{unit=3cm}
\begin{pspicture}(-0.3,-0.4)(.2,1)
  \psset{xAxisLabel=$t$,xAxisLabelPos={c,-6ex},yAxisLabelPos={-3ex,c}}
  \begin{psgraph}[axesstyle=frame,Ox=-1,](0,0)(0,0)(4,1){10cm}{2.5cm}
  \rput(1,0){\psplot[algebraic]{-1}{3}{Euler^(-x^2)}}
  \pstODEsolve[algebraicIC,algebraic]{TY}{(t) 0}{-1}{3}{5}{1/Euler}{-2*t*y[0]}
  \rput(1,0){\listplot[plotstyle=dots,dotsize=0.05,linecolor=red]{TY}}
  \end{psgraph}
\end{pspicture}
\end{center}
\end{document}