\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) = \left ( y \left ( t \right ) \right ) ^{2}-\cos \left ( x \left ( t \right ) \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =-y \left ( t \right ) \sin \left ( x \left ( t \right ) \right ) \right \} } \]
Mathematica: cpu = 250.096758 (sec), leaf count = 35 \[ \text {DSolve}\left [\left \{x'(t)=y(t)^2-\cos (x(t)),y'(t)=y(t) (-\sin (x(t)))\right \},\{x(t),y(t)\},t\right ] \]
Maple: cpu = 0.593 (sec), leaf count = 109 \[ \left \{ [ \left \{ x \left ( t \right ) ={\it RootOf} \left ( 2\,\int ^{{ \it \_Z}}\! \left ( \tan \left ( {\it RootOf} \left ( -3\,\sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}\ln \left ( 9/4\,{ \frac { \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +3\,{\it \_C1}\, \sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}+2\,{\it \_Z}\,\cos \left ( {\it \_f} \right ) \right ) \right ) \sqrt {-4\,\cos \left ( 2\,{\it \_f} \right ) -4- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}-\cos \left ( {\it \_f} \right ) \right ) ^{-1}{d{\it \_f} }+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) =\sqrt { {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) },y \left ( t \right ) =-\sqrt {{\frac {\rm d}{{\rm d} t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) } \right \} ] \right \} \]