Answer
$\frac{dy}{dt}=\frac{-2}{9}$
Work Step by Step
$\frac{x^{2}+5y}{x-2y}=2$
$x^{2}+5y=2x-2xy$
$2x\frac{dx}{dt}+5\frac{dy}{dt}=2\frac{dx}{dt}-2x\frac{dy}{dt}-2y\frac{dx}{dt}$
$(5+2x)\frac{dy}{dt}=(2-2x-2y)\frac{dx}{dt}$
Now substitute x=2; y=0; dx/dt=1
$9\frac{dy}{dt}=-2$
$\frac{dy}{dt}=\frac{-2}{9}$
