$\renewcommand{\Re}{\operatorname{Re}}$ $\renewcommand{\Im}{\operatorname{Im}}$ $\newcommand{\erf}{\operatorname{erf}}$ $\newcommand{\dag}{\dagger}$ $\newcommand{\const}{\mathrm{const}}$ $\newcommand{\arcsinh}{\operatorname{arcsinh}}$ ###[Problems](id:sect-2.2.P) > 1. [Problem 1](#problem-2.2.P.1) > 2. [Problem 2](#problem-2.2.P.2) **[Problem 1.](id:problem-2.2.P.1)** a. 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} b. Solve IVP $u(x,y,0)=f(x,y)$. **[Problem 2.](id:problem-2.2.P.2)** a. 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} b. Solve IVP $u(x,y,0)=0$. ______ [$\Uparrow$](../contents.html)  [$\uparrow$](./S2.2.html)  [$\Rightarrow$](./S2.3.html)