= Velocity reconstruction from the Orr-Sommerfeld vorticity
{title2=$\widehat v=C_+e^y+C_-e^{-y}+\int_{y_0}^y\sinh(y-s)W(s)\,ds$}
The equation $(D^2-1)\widehat v=W$ is inverted by the displayed formula: differentiating twice produces the endpoint contribution $W(y)$, since $\sinh0=0$ and $(\sinh)'(0)=1$. If $W=a_1\operatorname{Ai}(Z)+a_2\operatorname{Bi}(Z)$, there are four independent constants $C_+,C_-,a_1,a_2$. This reconstructs the velocity from the <Airy reduction of the Orr-Sommerfeld equation in constant shear>; four no-slip and no-flux conditions determine the boundary eigenproblem.
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