\[ y'(x)=\frac {-\frac {1}{2} x \sin (2 y(x))-\frac {1}{2} \sin (2 y(x))+\frac {1}{2} x \cos (2 y(x))+\frac {x}{2}}{x (x+1)} \] ✓ Mathematica : cpu = 0.479953 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {x-\log (x+1)-c_1}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.587 (sec), leaf count = 22
\[\left \{y \left (x \right ) = -\arctan \left (\frac {-c_{1}-x +\ln \left (x +1\right )}{x}\right )\right \}\]