PDE 9: Chaplygin equation

\[u_{xx}+\frac{y^2}{1-y^2/c^2}\,u_{yy}+y\,u_y=0 \]

where \(c\) is the speed of sound. In what situations does this problem arise? Your choice of boundary condition should reflect this.

Google: Chaplygin's equation, transonic flow.

Challenges: applications.