\[ y'(x)^2 \sin (y(x))+2 x y'(x) \cos ^3(y(x))-\sin (y(x)) \cos ^4(y(x))=0 \] ✗ Mathematica : cpu = 300.038 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 4.607 (sec), leaf count = 1134
\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {1}{2\,{\it \_T}} \left ( \left ( \cos \left ( {\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 ) }}}}},-9\,{\frac {1/3\, \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 \_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 ) }} \right ) \left ( {\it \_T}\,{\it \_C1}+1/9\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \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}}} \right ) } \right ) \right ) ^{4}-{{\it \_T}}^{2} \right ) \sin \left ( {\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 ) }}}}},-9\,{\frac {1/3\, \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 \_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 ) }} \right ) \left ( {\it \_T}\,{\it \_C1}+1/9\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \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}}} \right ) } \right ) \left ( \cos \left ( {\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 ) }}}}},-9\,{\frac {1/3\, \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 \_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 ) }} \right ) \left ( {\it \_T}\,{\it \_C1}+1/9\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \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}}} \right ) } \right ) \right ) ^{-3}},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 ) }}}}},-9\,{\frac {1/3\, \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 \_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 ) }} \right ) \left ( {\it \_T}\,{\it \_C1}+1/9\,\sqrt {3}\sqrt {{{\it \_C1}}^{2}{{\it \_T}}^{2} \left ( {{\it \_C1}}^{2}{{\it \_T}}^{2}+27 \right ) } \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}}} \right ) }] \right \} \]