= Solution
The nonzero factor $ab/D$ can be cancelled in the local <differential equation>, leaving $x\,dy-y\,dx=0$. On an interval with $x\ne0$,
$$
\frac{d}{dx}\left(\frac yx\right)=\frac{xy'-y}{x^2}=0.
$$
Hence the explicit <general solution> is
$$
\boxed{y(x)=Cx,\qquad C\in\mathbb R,}
$$
on any interval that avoids the excluded origin. It also follows from fixing the local angle potential, with slope $C=(a/b)\tan(f-C_0)$. As parameterized curves there are also vertical rays $x=0$, which cannot be represented as single-valued functions $y(x)$. Geometrically the connected <integral curves> are rays, not lines continued through the undefined origin.
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