Problems to Section 2.2

$\renewcommand{\Re}{\operatorname{Re}}$ $\renewcommand{\Im}{\operatorname{Im}}$ $\newcommand{\erf}{\operatorname{erf}}$ $\newcommand{\dag}{\dagger}$ $\newcommand{\const}{\mathrm{const}}$ $\newcommand{\arcsinh}{\operatorname{arcsinh}}$

Problems

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 $u(x,y,0)=f(x,y)$.

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 $u(x,y,0)=0$.

Problem 3.

  1. Find the general solution to each of the following equations \begin{gather} u_t + 3u_x -2u_y=u;\\ u_t + 3u_x -2u_y= xy u. \end{gather}
  2. Solve IVP $u(x,y,0)=f(x,y)$.

$\Uparrow$  $\uparrow$  $\Rightarrow$