%Linear First-order ODE's
%If you modify this file, please indicate here and in the footnote
%Math340

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\begin{center}
{\Large
Linear First-order Equations
\footnote{Copyright \copyright 2002 Larry Snyder and Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
\end{center}

\begin{enumerate}
\item Enter the following commands:
   \begin{enumerate}
      \item  \verb&y = dsolve('Dy=-0.1*y', 'y(0)=1')&
      \item  \verb&ezplot(y, [-20, 20])& 
      \item  Explain exactly what happened.
   \end{enumerate}

\item Repeat the above procedure to solve and plot the 
      solutions for the following differential equations. 
      Use the same initial condition as above.
\begin{enumerate}
      \item  $y'(t) = \sin(t)$
      \item  $y'(t) = -0.1 y + \sin(t)$
      \item\label{q2} Explain exactly what happened in each example. 
   \end{enumerate}

\item Compare the differential equations in the three examples.
      Then compare the graphs of the solutions in the three 
      examples. What do you observe from these comparisons?

\item Prepare a brief (\verb$< $1 page) written report answering all
      the questions and sketching the graphs carefully by hand. 
      Use complete sentences and standard mathematical notation. 
      Do {\bf not} get a printout.

\end{enumerate}

\vfill
\noindent
\textsf{Students observe that for linear
     differential equations qualitative features of solutions tend to "add"
     as terms are added to the righthand side.}

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