Solution (source code)

= Solution

With the convention
$$
u=\frac{\partial\psi}{\partial y},
\qquad
v=-\frac{\partial\psi}{\partial x},
$$
a <stream function> is
$$
\boxed{\psi(x,y)=\frac{y}{x^2+y^2}},
$$
up to an additive constant. Differentiation recovers both velocity components.