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\LARGE 

{\hspace{50mm}Quiz 8
\hspace{50mm}Name:\hspace{20mm}}


\large

Directions:  Answer each question to the best of your ability.  You may use a calculator, but you must show all work to receive full credit. 
\small

\begin{enumerate}
\item State the order of the following differential equation:  $(y'')^3-(y')^2+y^5=0$  (3 pts)
\vspace{7mm}
\item For what value of $k$, if any, is the equation $y=e^{kt}$ a solution to the differential equation, $y'''-27y=0$ for any value of $t$. (4 pts)
\vfill
\item Which of the following differential equations will produce the given slope field? (3 pts)
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\begin{enumerate}
\item $y'=xy$
\item $y'=x^2y$
\item $y'=xy^2$
\item $y'=x^2y^2$
\item None of the above
\end{enumerate}
\newpage
\item Using Euler's method, approximate $y(4)$ using 2 steps given the differential equation $y'=y$ and the initial condition that $y(0)=2$.  (5 pts)
\vfill
\item What is the actual value of $y(4)$ from the previous problem? (5 pts)
\vfill
\item Find the solution to the differential equation, $y'=y+1$ containing the point (0,0).  (5 pts)
\vfill

\end{enumerate}

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