\[ y'(x)=\frac {\cos (y(x)) \left (x^3 \cos (y(x))-x-1\right )}{(x+1) (x \sin (y(x))-1)} \] ✓ Mathematica : cpu = 0.212125 (sec), leaf count = 849
DSolve[Derivative[1][y][x] == (Cos[y[x]]*(-1 - x + x^3*Cos[y[x]]))/((1 + x)*(-1 + x*Sin[y[x]])),y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {6 \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)},x-\frac {\left (2 x^3-3 x^2+6 x+6 c_1-6 \log (x+1)\right ) \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )\right \},\left \{y(x)\to \tan ^{-1}\left (-\frac {6 \left (-2 x^4+3 x^3-6 x^2-6 c_1 x+6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)},x-\frac {\left (2 x^3-3 x^2+6 x+6 c_1-6 \log (x+1)\right ) \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x-\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )\right \}\right \}\] ✓ Maple : cpu = 2.487 (sec), leaf count = 723
dsolve(diff(y(x),x) = cos(y(x))/(x*sin(y(x))-1)*(cos(y(x))*x^3-x-1)/(1+x),y(x))
\[y \left (x \right ) = \arctan \left (\frac {\left (-2 x^{3}+3 x^{2}-6 x -6 c_{1}+6 \ln \left (1+x \right )\right ) \sqrt {36 \ln \left (1+x \right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (1+x \right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}-36 x^{2} c_{1}+72 x c_{1}+36 c_{1}^{2}+36}+36 x}{36 \ln \left (1+x \right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (1+x \right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+\left (-36 c_{1}+36\right ) x^{2}+72 x c_{1}+36 c_{1}^{2}+36}, \frac {12 x^{4}-18 x^{3}+36 x^{2}+36 x c_{1}-36 \ln \left (1+x \right ) x +6 \sqrt {36 \ln \left (1+x \right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (1+x \right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}-36 x^{2} c_{1}+72 x c_{1}+36 c_{1}^{2}+36}}{36 \ln \left (1+x \right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (1+x \right )+4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+\left (-36 c_{1}+36\right ) x^{2}+72 x c_{1}+36 c_{1}^{2}+36}\right )\]