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\begin{document}
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{\newpage
\clearpage
\samepage \begin{displaymath}y''=-y'+\sin (ty) \hspace{.2in} y(0)=1, y'(0)=2
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y'=v
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}v'=-v+\sin(ty)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}z_{k+1}=z_k+\Delta tw_k
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}w_{k+1}=w_k+\Delta t\{-w_k+\sin(t_kz_k)\}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y''=f(t,y,y') \hspace{.2in}y(t_0)=y_0, y'(t_0)=y'_0.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y'=v \hspace{.2in} y(t_0)=y_0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}v'=f(t,y,v) \hspace{.2in} y(t_0)=y'_0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}z_{k+1}=z_k+(t_{k+1}-t_k)v_k \hspace{.2in} z_0=y_0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}v_{k+1}=v_k+(t_{k+1}-t_k)f(t,z_k,v_k) \hspace{.2in} v_0=y'_0
\end{displaymath}
}

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\end{document}
