\documentclass[minion]{homework}
\newcommand{\Reals}{\mathbb{R}}
\doclabel{Math F615: Homework 9}
\docdate{Due: April 5, 2021}
\usepackage{graphicx}
\usepackage{enumerate}
\newcommand{\bfx}{\mathbf{x}}
\newcommand{\bfv}{\mathbf{v}}

\begin{document}

\begin{problems}

\problem  Text, 4.12

\problem Text, 4.17

\problem Consider the equation
\[
u_t + a u_{x} - b u_{xxx} = 0
\]
where $x\in \Reals$.  Suppose at $t=0$, $u(x,t)=e^{ikx}$.
Find a solution of the differential equation. Describe the
solution as a traveling wave.  What is the speed of the wave?
How does the speed change as we change the spatial frequency $k$?


\end{problems}

\end{document}