%Linear First-order ODE's %If you modify this file, please indicate here and in the footnote %Math340 \documentclass[12pt]{article} \usepackage{times} \pagestyle{empty} \addtolength{\textwidth}{1.2in} \addtolength{\textheight}{1.2in} \addtolength{\oddsidemargin}{-.58in} \addtolength{\evensidemargin}{-.58in} \renewcommand{\baselinestretch}{1.0} \parindent = 0cm \parskip = .1cm \begin{document} \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.} \end{document}