\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}\sin \left ( y \left ( x \right ) \right ) +2\,x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \left ( \cos \left ( y \left ( x \right ) \right ) \right ) ^{3}-\sin \left ( y \left ( x \right ) \right ) \left ( \cos \left ( y \left ( x \right ) \right ) \right ) ^{4}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.748 (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 ( \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 ) +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 ) \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 \} \]