\left\{x''(t)=a e^{2 x(t)}+e^{-2 x(t)} \cos ^2(y(t))-e^{-x(t)},y''(t)=e^{-2 x(t)} \sin (y(t)) \cos (y(t))-\tan (y(t)) \sec ^2(y(t))\right\}