Solution
= Solution
Let $F(p)=2p/(1-p^2)$, so that $y=xF(p)$. Differentiation gives
$$
p=\frac{2p}{1-p^2}
+x\frac{2(1+p^2)}{(1-p^2)^2}\frac{dp}{dx}.
$$
Move the first term to the left and use
$$
p-\frac{2p}{1-p^2}=-\frac{p(1+p^2)}{1-p^2}.
$$
Since $1+p^2>0$ for real $p$ and $p\ne\pm1$, cancellation gives
$$
\boxed{2x\frac{dp}{dx}=-p(1-p^2)}.
$$
This is the <slope parameter for a homogeneous first-order equation> reduction.