Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 1 / 12 / b / iii / Solution

The nonzero factor $ab/D$ can be cancelled in the local differential equation, leaving $xdy-ydx=0$. On an interval with $x\ne 0$,Hence the explicit general solution ison 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.