\[ y'(x)=\frac {-\frac {1}{2} x \sin (2 y(x))-\frac {1}{2} \sin (2 y(x))+\frac {1}{2} x \cos (2 y(x))+\frac {x}{2}}{x (x+1)} \] ✓ Mathematica : cpu = 0.426154 (sec), leaf count = 22
DSolve[Derivative[1][y][x] == (x/2 + (x*Cos[2*y[x]])/2 - Sin[2*y[x]]/2 - (x*Sin[2*y[x]])/2)/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {x-\log (x+1)-c_1}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.692 (sec), leaf count = 22
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))*x-sin(2*y(x))+x*cos(2*y(x))+x)/x/(1+x),y(x))
\[y \left (x \right ) = -\arctan \left (\frac {\ln \left (1+x \right )-x -c_{1}}{x}\right )\]