\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {\cos \left ( y \left ( x \right ) \right ) \left ( \cos \left ( y \left ( x \right ) \right ) {x}^{3}-x-1 \right ) }{ \left ( x\sin \left ( y \left ( x \right ) \right ) -1 \right ) \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 19.954034 (sec), leaf count = 39 \[ \text {DSolve}\left [y'(x)=\frac {\cos (y(x)) \left (x^3 \cos (y(x))-x-1\right )}{(x+1) (x \sin (y(x))-1)},y(x),x\right ] \]
Maple: cpu = 1.060 (sec), leaf count = 874 \[ \left \{ y \left ( x \right ) =\arctan \left ( -{\frac {-2\,{x}^{3}+3\,{x }^{2}+6\,\ln \left ( 1+x \right ) -6\,{\it \_C1}-6\,x}{4\,{x}^{6}-12\,{ x}^{5}+24\,{\it \_C1}\,{x}^{3}+33\,{x}^{4}-24\,\ln \left ( 1+x \right ) {x}^{3}-36\,{x}^{2}{\it \_C1}-36\,{x}^{3}+36\,\ln \left ( 1+x \right ) {x}^{2}+36\,{{\it \_C1}}^{2}+72\,{\it \_C1}\,x-72\,{\it \_C1} \,\ln \left ( 1+x \right ) +36\,{x}^{2}-72\,\ln \left ( 1+x \right ) x+ 36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+36} \left ( -2\,{x}^{ 4}+3\,{x}^{3}+6\,\ln \left ( 1+x \right ) x-6\,{\it \_C1}\,x-6\,{x}^{2} +\sqrt {4\,{x}^{6}-12\,{x}^{5}-24\,\ln \left ( 1+x \right ) {x}^{3}+24 \,{\it \_C1}\,{x}^{3}+33\,{x}^{4}+36\,\ln \left ( 1+x \right ) {x}^{2}- 36\,{x}^{2}{\it \_C1}-36\,{x}^{3}+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}-72\,{\it \_C1}\,\ln \left ( 1+x \right ) -72\,\ln \left ( 1+x \right ) x+36\,{{\it \_C1}}^{2}+72\,{\it \_C1}\,x+36} \right ) }+x,-6\,{\frac {-2\,{x}^{4}+3\,{x}^{3}+6\,\ln \left ( 1+x \right ) x-6\,{\it \_C1}\,x-6\,{x}^{2}+\sqrt {4\,{x}^{6}-12\,{x}^{5}- 24\,\ln \left ( 1+x \right ) {x}^{3}+24\,{\it \_C1}\,{x}^{3}+33\,{x}^{4 }+36\,\ln \left ( 1+x \right ) {x}^{2}-36\,{x}^{2}{\it \_C1}-36\,{x}^{3 }+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}-72\,{\it \_C1}\, \ln \left ( 1+x \right ) -72\,\ln \left ( 1+x \right ) x+36\,{{\it \_C1} }^{2}+72\,{\it \_C1}\,x+36}}{4\,{x}^{6}-12\,{x}^{5}+24\,{\it \_C1}\,{x }^{3}+33\,{x}^{4}-24\,\ln \left ( 1+x \right ) {x}^{3}-36\,{x}^{2}{\it \_C1}-36\,{x}^{3}+36\,\ln \left ( 1+x \right ) {x}^{2}+36\,{{\it \_C1}} ^{2}+72\,{\it \_C1}\,x-72\,{\it \_C1}\,\ln \left ( 1+x \right ) +36\,{x }^{2}-72\,\ln \left ( 1+x \right ) x+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+36}} \right ) ,y \left ( x \right ) =\arctan \left ( {\frac {-2\,{x}^{3}+3\,{x}^{2}+6\,\ln \left ( 1+x \right ) -6\, {\it \_C1}-6\,x}{4\,{x}^{6}-12\,{x}^{5}+24\,{\it \_C1}\,{x}^{3}+33\,{x }^{4}-24\,\ln \left ( 1+x \right ) {x}^{3}-36\,{x}^{2}{\it \_C1}-36\,{x }^{3}+36\,\ln \left ( 1+x \right ) {x}^{2}+36\,{{\it \_C1}}^{2}+72\,{ \it \_C1}\,x-72\,{\it \_C1}\,\ln \left ( 1+x \right ) +36\,{x}^{2}-72\, \ln \left ( 1+x \right ) x+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+36} \left ( 2\,{x}^{4}-3\,{x}^{3}-6\,\ln \left ( 1+x \right ) x+6\,{\it \_C1}\,x+6\,{x}^{2}+\sqrt {4\,{x}^{6}-12\,{x}^{5}- 24\,\ln \left ( 1+x \right ) {x}^{3}+24\,{\it \_C1}\,{x}^{3}+33\,{x}^{4 }+36\,\ln \left ( 1+x \right ) {x}^{2}-36\,{x}^{2}{\it \_C1}-36\,{x}^{3 }+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}-72\,{\it \_C1}\, \ln \left ( 1+x \right ) -72\,\ln \left ( 1+x \right ) x+36\,{{\it \_C1} }^{2}+72\,{\it \_C1}\,x+36} \right ) }+x,6\,{\frac {2\,{x}^{4}-3\,{x}^{ 3}-6\,\ln \left ( 1+x \right ) x+6\,{\it \_C1}\,x+6\,{x}^{2}+\sqrt {4\, {x}^{6}-12\,{x}^{5}-24\,\ln \left ( 1+x \right ) {x}^{3}+24\,{\it \_C1} \,{x}^{3}+33\,{x}^{4}+36\,\ln \left ( 1+x \right ) {x}^{2}-36\,{x}^{2}{ \it \_C1}-36\,{x}^{3}+36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2 }-72\,{\it \_C1}\,\ln \left ( 1+x \right ) -72\,\ln \left ( 1+x \right ) x+36\,{{\it \_C1}}^{2}+72\,{\it \_C1}\,x+36}}{4\,{x}^{6}-12\, {x}^{5}+24\,{\it \_C1}\,{x}^{3}+33\,{x}^{4}-24\,\ln \left ( 1+x \right ) {x}^{3}-36\,{x}^{2}{\it \_C1}-36\,{x}^{3}+36\,\ln \left ( 1+x \right ) {x}^{2}+36\,{{\it \_C1}}^{2}+72\,{\it \_C1}\,x-72\,{\it \_C1} \,\ln \left ( 1+x \right ) +36\,{x}^{2}-72\,\ln \left ( 1+x \right ) x+ 36\, \left ( \ln \left ( 1+x \right ) \right ) ^{2}+36}} \right ) \right \} \]