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\begin{document}
\pagestyle{empty}
{\newpage
\clearpage
\samepage \begin{displaymath}y''+\frac{p}{t}y'+\frac{q}{t^2}y=0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=C_1y_1(t)+C_2y_2(t)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}t^2y''+pty'+qy=0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y=t^r
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y'=rt^{r-1} \hspace{.2in} y''=r(r-1)t^{r-2}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}t^2r(r-1)t^{r-2}+ptrt^{r-1}+qt^r=t^r(r(r-1)+pr+q)=0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}F(r)=r^2+pr+q=0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t) = C_1|t|^a+C_2|t|^b
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y''-2y'-18y=0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=C_1|t|^6+C_2|t|^{-3}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=C_1|t|^a+C_2|t|^a\log(|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y'' + 7y' + 9y = 0.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t) = C_1|t|^{-3}+C_2|t|^{-3}\log(|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t) = C_1|t|^{a+ib}+C_2|t|^{a-ib} 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}|t|^{ib}=e^{ib\log|t|}=\cos(b\log|t|)+i\sin(b\log|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}|t|^{a+ib}=|t|^a|t|^{ib}=|t|^a(\cos(b\log|t|)+i\sin(b\log|t|))
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}|t|^{a-ib}=|t|^a|t|^{-ib}=|t|^a(\cos(b\log|t|)-i\sin(b\log|t|))
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t) = C_1|t|^a(\cos(b\log|t|)+i\sin(b\log|t|)) + 
C_2|t|^a(\cos(b\log|t|)-i\sin(b\log|t|))
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=|t|^a}\cos(b\log|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=|t|^a\sin(b\log|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t) = D_1|t|^a\cos(b\log|t|) + D_2|t|^a\sin(b\log|t|)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y'' - 6y' + 13 = 0
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y(t)=D_1|t|^3\cos(2\log|t|)+D_2|t|^3\sin(2\log|t|)
\end{displaymath}
}

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\end{document}
