= Solution
{c}
For a profile depending only on $y$, the <Poisson equation> becomes $w_1''=-G/\mu$. Integrating twice gives
$$
w_1(y)=-\frac{G}{2\mu}y^2+C_1y+C_2.
$$
The <no-slip boundary conditions> $w_1(b)=w_1(-b)=0$ imply $C_1=0$ and $C_2=Gb^2/(2\mu)$. Thus
$$
\boxed{w_1(y)=\frac{G}{2\mu}(b^2-y^2).}
$$
This is <plane Poiseuille flow> between the two horizontal walls. It is positive in the interior for $G>0$, so the <velocity> points down the <pressure gradient>. It does not satisfy the side-wall <no-slip boundary conditions>, which is precisely what the correction in part (iii) repairs.
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