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\begin{document}

{\bf Question}

Classify (give order etc.) each of the following partial
differential equations

\begin{description}
\item[(a)]
$u_{xx}+u_{yy}=7u_x$

\item[(b)]
$u_{xx}+x^2u_x=y^2u_y$

\item[(c)]
$uu_x+u_y=xu$

\item[(d)]
$u_x+u_y=x$

\item[(e)]
$e^xu_x+e^yu_y=u^2$

\item[(f)]
$\bigtriangledown^2(\bigtriangledown^2 u)=u_{xx}$

\item[(g)]
$(x^3u_{xx})_x=(y^{-2}u_y)_y$
\end{description}

\medskip

{\bf Answer}

\begin{description}
\item[(a)]
Second order, linear, homogeneous, constant coefficients

\item[(b)]
Second order, linear, homogeneous, constant coefficients

\item[(c)]
First order, quasi-linear

\item[(d)]
First order, linear

\item[(e)]
First order, quasi-linear

\item[(f)]
Fourth order, linear, homogeneous, constant coefficients

\item[(g)]
Third order, linear, homogeneous, constant coefficients

\end{description}

\end{document}
