$\renewcommand{\Re}{\operatorname{Re}}$ $\renewcommand{\Im}{\operatorname{Im}}$ $\newcommand{\erf}{\operatorname{erf}}$ $\newcommand{\dag}{\dagger}$ $\newcommand{\const}{\mathrm{const}}$ $\newcommand{\arcsinh}{\operatorname{arcsinh}}$
**<span id="problem-2.2.P.1"></span>Problem 1.**
1. Find the general solution to each of the following equations
\begin{gather}
u\_t + 3u\_x -2u\_y=0;\\\\
u\_t + xu\_x+ yu\_y=0;\\\\
u\_t + xu\_x- yu\_y=0;\\\\
u\_t + yu\_x+ xu\_y=0;\\\\
u\_t + yu\_x-xu\_y=0.
\end{gather}
2. Solve IVP $u(x,y,0)=f(x,y)$.
**<span id="problem-2.2.P.2"></span>Problem 2.**
1. Find the general solution to each of the following equations
\begin{gather}
u\_t + 3u\_x -2u\_y=x;\\\\
u\_t + xu\_x+ yu\_y=x;\\\\
u\_t + xu\_x- yu\_y=x;\\\\
u\_t + yu\_x+ xu\_y=x;\\\\
u\_t + yu\_x-xu\_y=x.
\end{gather}
2. Solve IVP $u(x,y,0)=0$.
**<span id="problem-2.2.P.3"></span>Problem 3.**
1. Find the general solution to each of the following equations
\begin{gather}
u\_t + 3u\_x -2u\_y=u;\\\\
u\_t + xu\_x+ yu\_y=u;\\\\
u\_t + xu\_x- yu\_y=u;\\\\
u\_t + yu\_x+ xu\_y=u;\\\\
u\_t + yu\_x-xu\_y=u;\\\\
u\_t + 3u\_x -2u\_y= xy u.
\end{gather}
2. Solve IVP $u(x,y,0)=f(x,y)$.