\[ y'(x)=-\frac {(-\cos (y(x))+x+1) \cos (y(x))}{(x+1) (x \sin (y(x))-1)} \] ✓ Mathematica : cpu = 5.9824 (sec), leaf count = 221
\[\left \{\left \{y(x)\to -\sec ^{-1}\left (\frac {-\sqrt {2 c_1 \log (x+1)+c_1^2-x^2+\log ^2(x+1)+1}+c_1 x+x \log (x+1)}{x^2-1}\right )\right \},\left \{y(x)\to \sec ^{-1}\left (\frac {-\sqrt {2 c_1 \log (x+1)+c_1^2-x^2+\log ^2(x+1)+1}+c_1 x+x \log (x+1)}{x^2-1}\right )\right \},\left \{y(x)\to -\sec ^{-1}\left (\frac {\sqrt {2 c_1 \log (x+1)+c_1^2-x^2+\log ^2(x+1)+1}+c_1 x+x \log (x+1)}{x^2-1}\right )\right \},\left \{y(x)\to \sec ^{-1}\left (\frac {\sqrt {2 c_1 \log (x+1)+c_1^2-x^2+\log ^2(x+1)+1}+c_1 x+x \log (x+1)}{x^2-1}\right )\right \}\right \}\]
✓ Maple : cpu = 1.905 (sec), leaf count = 239
\[ \left \{ y \left ( x \right ) =\arctan \left ( {\frac {1}{{{\it \_C1}}^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) + \left ( \ln \left ( 1+x \right ) \right ) ^{2}+1} \left ( \left ( -\ln \left ( 1+x \right ) +{\it \_C1} \right ) \sqrt { \left ( \ln \left ( 1+x \right ) \right ) ^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) +{{\it \_C1}}^{2}-{x}^{2}+1}+x \right ) },{\frac {1}{{{\it \_C1}}^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) + \left ( \ln \left ( 1+x \right ) \right ) ^{2}+1} \left ( \ln \left ( 1+x \right ) x-x{\it \_C1}+\sqrt { \left ( \ln \left ( 1+x \right ) \right ) ^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) +{{\it \_C1}}^{2}-{x}^{2}+1} \right ) } \right ) ,y \left ( x \right ) =\arctan \left ( {\frac {1}{{{\it \_C1}}^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) + \left ( \ln \left ( 1+x \right ) \right ) ^{2}+1} \left ( \left ( \ln \left ( 1+x \right ) -{\it \_C1} \right ) \sqrt { \left ( \ln \left ( 1+x \right ) \right ) ^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) +{{\it \_C1}}^{2}-{x}^{2}+1}+x \right ) },{\frac {1}{{{\it \_C1}}^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) + \left ( \ln \left ( 1+x \right ) \right ) ^{2}+1} \left ( -x{\it \_C1}+\ln \left ( 1+x \right ) x-\sqrt { \left ( \ln \left ( 1+x \right ) \right ) ^{2}-2\,{\it \_C1}\,\ln \left ( 1+x \right ) +{{\it \_C1}}^{2}-{x}^{2}+1} \right ) } \right ) \right \} \]