11.5.5.15 Mixed problems
Problem:
Solve the external Dirichlet boundary-value problem for the circle:
\[
\begin{array}{l}
\Delta u(r, \varphi)=0, \quad r>r_{0}, \quad 0 \leq \varphi<2 \pi, \\
|u(r, \varphi)|<+\infty, \quad u\left(r_{0}, \varphi\right)=\frac{u_{0} \sin \varphi}{25+7 \cos \varphi} .
\end{array}
\]