Can the system

$\displaystyle m\dfrac{d^2 x}{dt^2}=-k \dfrac{dx}{dt} \sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{d y}{dt}\right)^2}$

$\displaystyle m \dfrac{d^2 y}{dt^2}+mg=-k \dfrac{dy}{dt} \sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{d y}{dt}\right)^2}$

be solved explicitly? Where $\displaystyle m$, $\displaystyle g$ and $\displaystyle k$ are constants and the functions $\displaystyle x$ and $\displaystyle y$ depend only on $\displaystyle t$