\[
\boxed{
 \left\{ {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left( t \right) =a{{\rm e}^{2\,x \left( t \right) }}-{{\rm e}^{-x \left( t \right) }}+{{\rm e}^{-2\,x \left( t \right) }} \left( \cos \left( y \left( t \right)  \right)  \right) ^{2},{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left( t \right) ={{\rm e}^{-2\,x \left( t \right) }}\sin \left( y \left( t \right)  \right) \cos \left( y \left( t \right)  \right) -{\frac {\sin \left( y \left( t \right)  \right) }{ \left( \cos \left( y \left( t \right)  \right)  \right) ^{3}}} \right\} }
\]