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\centerline{\textbf{\large QUIZ}}

\vspace*{.2in}

\textbf{MATxxx - Semester 200x  \hspace*{1.5in} NAME \hrulefill}

\vspace*{.2in}

\textbf{TTH ??:??-??:??   \hspace*{2.4in} I.D. \hrulefill}

\vspace*{0.6in}

Consider the IVP
$$                      % CAN ALSO USE \[
\left\{
\begin{array}{l}
   t^2y''-ty'-3y=0 \\
   y(1)=2, \hspace*{3pt} y'(1)=2
\end{array}
\right.
$$                      % CAN ALSO USE \]

\begin{enumerate}
\item
What is the maximal interval on which you can guarantee the existence
of a solution?

\vspace*{3.0in}

\item
Verify that the functions $y_1(t)=t^3$ and $y_2(t)=\frac{1}{t}$ are
solutions of the ODE for $t>0$.

\end{enumerate}

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