Answer
The equilibrium points are $(\dfrac{c}{d},\dfrac{a}{b})$ and $(0,0)$
Work Step by Step
$\dfrac{dx}{dt}=(a-by) x$
Also, $\dfrac{dy}{dt}=(-c+dx) x$
Consider $\dfrac{dx}{dt}=0$
$(a-by) x =0 \implies y=\dfrac{a}{b}$ and $x=0$
Next, consider $\dfrac{dy}{dt}=0$
$(-c+dx) x =0 \implies x=\dfrac{c}{d}$ and $y=0$
Hence, the equilibrium points are $(\dfrac{c}{d},\dfrac{a}{b})$ and (0,0).
Thus, we can see that at the equilibrium points, the rabbit or prey and foxes or, perpetrator population remains constant.
