\[ y'(x)^2 \sin (y(x))+2 x y'(x) \cos ^3(y(x))-\sin (y(x)) \cos ^4(y(x))=0 \] ✗ Mathematica : cpu = 300.034 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 2.542 (sec), leaf count = 2402
\[ \left \{ [x \left ( {\it \_T} \right ) =-{\frac {1}{8\,{\it \_T}} \left ( 16\,{{\it \_T}}^{2}\sin \left ( 1/2\,\arctan \left ( {\frac {{{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}},{\frac {-\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}} \right ) \right ) -2\,\sin \left ( 1/2\,\arctan \left ( {\frac {{{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}},{\frac {-\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}} \right ) \right ) -\sin \left ( {\frac {5}{2}\arctan \left ( {1 \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}}},{1 \left ( -\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3} \right ) \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{-{\frac {2}{3}}}} \right ) } \right ) -3\,\sin \left ( 3/2\,\arctan \left ( {\frac {{{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}},{\frac {-\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}} \right ) \right ) \right ) \left ( 3\,\cos \left ( 1/2\,\arctan \left ( {\frac {{{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}},{\frac {-\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}{ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3}}} \right ) \right ) +\cos \left ( {\frac {3}{2}\arctan \left ( {1 \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}}},{1 \left ( -\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3} \right ) \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{-{\frac {2}{3}}}} \right ) } \right ) \right ) ^{-1}},y \left ( {\it \_T} \right ) ={\frac {1}{2}\arctan \left ( {1 \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}-2\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+ \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}}}},{1 \left ( -\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }{\it \_T}\,{\it \_C1}-9\,{{\it \_C1}}^{2}{{\it \_T}}^{2}+\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}+9\,{\it \_T}\,{\it \_C1}\,\sqrt [3]{{{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) }}-3\, \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{2/3} \right ) \left ( {{\it \_C1}}^{3}{{\it \_T}}^{3}+54\,{\it \_T}\,{\it \_C1}+6\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \right ) ^{-{\frac {2}{3}}}} \right ) }] \right \} \]