Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 2 / 14 / c / i / Solution

Let $F(p)=2p/(1-p^2)$, so that $y=xF(p)$. Differentiation givesMove the first term to the left and useSince $1+p^2>0$ for real $p$ and $p\ne \pm 1$, cancellation givesThis is the slope parameter for a homogeneous first-order equation reduction.