\[ \left \{x'(t)=y(t)^2-\cos (x(t)),y'(t)=y(t) (-\sin (x(t)))\right \} \] ✓ Mathematica : cpu = 209.692 (sec), leaf count = 3406
\[\left \{\left \{y(t)\to \frac {3 \sqrt [3]{2} \cos \left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3}}{2\ 2^{2/3} \cos ^2(K[1])+2 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3} \cos (K[1])+3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}+\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[1])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}}dK[1]\& \right ]\left [\frac {t}{2}+c_2\right ]\right )}{\sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3}}{2\ 2^{2/3} \cos ^2(K[1])+2 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3} \cos (K[1])+3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}+\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[1])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}}dK[1]\& \right ]\left [\frac {t}{2}+c_2\right ]\right )}}}+\frac {\sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3}}{2\ 2^{2/3} \cos ^2(K[1])+2 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3} \cos (K[1])+3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}+\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[1])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}}dK[1]\& \right ]\left [\frac {t}{2}+c_2\right ]\right )}}}{3 \sqrt [3]{2}},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3}}{2\ 2^{2/3} \cos ^2(K[1])+2 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}\right ){}^{2/3} \cos (K[1])+3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}+\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[1])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[1])}}}dK[1]\& \right ]\left [\frac {t}{2}+c_2\right ]\right \},\left \{y(t)\to -\frac {3 \left (1+i \sqrt {3}\right ) \cos \left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3}}{2 i 2^{2/3} \sqrt {3} \cos ^2(K[2])-2\ 2^{2/3} \cos ^2(K[2])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3} \cos (K[2])-3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}}dK[2]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}{2^{2/3} \sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3}}{2 i 2^{2/3} \sqrt {3} \cos ^2(K[2])-2\ 2^{2/3} \cos ^2(K[2])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3} \cos (K[2])-3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}}dK[2]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3}}{2 i 2^{2/3} \sqrt {3} \cos ^2(K[2])-2\ 2^{2/3} \cos ^2(K[2])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3} \cos (K[2])-3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}}dK[2]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}}}{6 \sqrt [3]{2}},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3}}{2 i 2^{2/3} \sqrt {3} \cos ^2(K[2])-2\ 2^{2/3} \cos ^2(K[2])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}\right ){}^{2/3} \cos (K[2])-3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[2])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[2])}}}dK[2]\& \right ]\left [\frac {t}{4}+c_2\right ]\right \},\left \{y(t)\to -\frac {3 \left (1-i \sqrt {3}\right ) \cos \left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3}}{-2 i 2^{2/3} \sqrt {3} \cos ^2(K[3])-2\ 2^{2/3} \cos ^2(K[3])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3} \cos (K[3])+3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}+i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}}dK[3]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}{2^{2/3} \sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3}}{-2 i 2^{2/3} \sqrt {3} \cos ^2(K[3])-2\ 2^{2/3} \cos ^2(K[3])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3} \cos (K[3])+3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}+i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}}dK[3]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{81 c_1+\sqrt {6561 c_1{}^2-2916 \cos ^3\left (\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3}}{-2 i 2^{2/3} \sqrt {3} \cos ^2(K[3])-2\ 2^{2/3} \cos ^2(K[3])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3} \cos (K[3])+3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}+i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}}dK[3]\& \right ]\left [\frac {t}{4}+c_2\right ]\right )}}}{6 \sqrt [3]{2}},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3}}{-2 i 2^{2/3} \sqrt {3} \cos ^2(K[3])-2\ 2^{2/3} \cos ^2(K[3])+4 \left (3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}\right ){}^{2/3} \cos (K[3])+3 i \sqrt [3]{2} \sqrt {3} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-3 \sqrt [3]{2} c_1 \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}+i \sqrt [3]{2} \sqrt {3} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}-\sqrt [3]{2} \sqrt {9 c_1{}^2-4 \cos ^3(K[3])} \sqrt [3]{3 c_1+\sqrt {9 c_1{}^2-4 \cos ^3(K[3])}}}dK[3]\& \right ]\left [\frac {t}{4}+c_2\right ]\right \}\right \}\] ✓ Maple : cpu = 1.614 (sec), leaf count = 108
\[ \left \{ [ \left \{ x \left ( t \right ) ={\it RootOf} \left ( -2\,\int ^{{\it \_Z}}\! \left ( -\tan \left ( {\it RootOf} \left ( -3\,\sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}\ln \left ( 9/4\,{\frac { \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}{ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +3\,{\it \_C1}\,\sqrt {- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}+2\,{\it \_Z}\,\cos \left ( {\it \_f} \right ) \right ) \right ) \sqrt {-4\,\cos \left ( 2\,{\it \_f} \right ) -4- \left ( \cos \left ( {\it \_f} \right ) \right ) ^{2}}+\cos \left ( {\it \_f} \right ) \right ) ^{-1}{d{\it \_f}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) =\sqrt {{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) },y \left ( t \right ) =-\sqrt {{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +\cos \left ( x \left ( t \right ) \right ) } \right \} ] \right \} \]