= Solution
{c}
With $u=xf'(\zeta)$ and $W=-f(\zeta)$, <incompressibility> is automatic because $u_x=f'$ and $W_\zeta=-f'$. In the streamwise <boundary-layer equation>,
$$
u u_x+W u_\zeta=x(f')^2-xff'',\qquad
u_{\zeta\zeta}=xf'''.
$$
Equating coefficients of $x$ gives
$$
(f')^2-ff''=1+f''',\qquad
\boxed{f'''+ff''+1-(f')^2=0.}
$$
This coefficient comparison determines the equation even though the streamwise equation vanishes identically at the <stagnation point> $x=0$.
The <no-penetration boundary condition> gives $f(0)=0$, the surface <shear stress> gives $xf''(0)=\gamma x$, and matching the tangential <velocity> to the <outer solution> gives $f'\to1$. Thus
$$
\boxed{f(0)=0,\qquad f''(0)=\gamma,\qquad
f'(\zeta)\longrightarrow1\quad(\zeta\to-\infty).}
$$
If the correction $f'-1$ is integrable at the far end, then $f=\zeta+O(1)$ there, which is consistent with $W\sim-\zeta$. The small-<shear stress> solution below has precisely this property.
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