\[ \left \{x'(t)=y(t)^2-\cos (x(t)),y'(t)=y(t) (-\sin (x(t)))\right \} \] ✗ Mathematica : cpu = 250.054 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == -Cos[x[t]] + y[t]^2, Derivative[1][y][t] == -(Sin[x[t]]*y[t])}, {x[t], y[t]}, t]
✓ Maple : cpu = 1.519 (sec), leaf count = 109
\[ \left \{ [ \left \{ x \left ( t \right ) ={\it RootOf} \left ( 2\,\int ^{{\it \_Z}}\! \left ( \tan \left ( {\it RootOf} \left ( -3\,\sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}\ln \left ( 9/4\,{\frac { \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +3\,{\it \_C1}\,\sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}+2\,{\it \_Z}\,\cos \left ( {\it \_f} \right ) \right ) \right ) \sqrt {-4\,\cos \left ( 2\,{\it \_f} \right ) -4- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}-\cos \left ( {\it \_f} \right ) \right ) ^{-1}{d{\it \_f}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) =\sqrt {{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) },y \left ( t \right ) =-\sqrt {{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) } \right \} ] \right \} \]