1. Solution.
  2. Consider the differential equation \begin{equation} x^2 z_x+α x y z_y=z^2 \end{equation} for α a real parameter and with $z=1$ on the data curve $x^2+y^2=1$. Solution.
  3. Let $D=\left\{x>0, y>0: x^2+y^2<1\right\}$ be the intersection of the positive quadrant with the open unit disk, and $u(x, y)$ be a twice continuously differentiable function on $\bar{D}=\{x ⩾ 0, y ⩾\left.0: x^2+y^2 ⩽ 1\right\}$
    Error! Click to view log. Solution.