\[ y'(x)=\frac {-\frac {1}{2} x \sin (2 y(x))-\frac {1}{2} \sin (2 y(x))+\frac {1}{2} x \cos (2 y(x))+\frac {x}{2}}{x (x+1)} \] ✓ Mathematica : cpu = 0.257519 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {-c_1+x-\log (x+1)}{x}\right )\right \}\right \}\]
✓ Maple : cpu = 0.674 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) =-\arctan \left ( {\frac {-x+\ln \left ( 1+x \right ) -{\it \_C1}}{x}} \right ) \right \} \]