Answer
$\dfrac{dp}{dq}=-\dfrac{10 p^2 q +p}{q+10pq^2}$
Work Step by Step
We have: $q^2 -pq=5p^2 q^2$
We differentiate both sides with respect to $q$.
$2q-(p+q\dfrac{dp}{dq}) =5[p^2 (2q) +q^2(2p)\dfrac{dp}{dq}] \\ 2q-p-q\dfrac{dp}{dq}=10p^2 q+10 pq^2 \dfrac{dp}{dq}\\(-q -10 pq^2) \dfrac{dp}{dq}=10 p^2 q +p\\\dfrac{dp}{dq}=-\dfrac{10 p^2 q +p}{q+10pq^2}$
