\begin{equation} \dot{x}(t)=\left(1-\frac{x(t)}{E_{0}}\right) x(t) - a\ y(t) \end{equation} \begin{equation} \dot{y}(t)=\left(1-\frac{a\ y(t)}{x(t)}\right) y(t) \end{equation}
I am trying to solve the system of differential equations above, but (I think) it is nontrivial to calculate its solution. Any suggestions?