\[ y'(x)=\frac {\frac {1}{2} x^4 \cos (2 y(x))+\frac {x^4}{2}-\frac {1}{2} x \sin (2 y(x))-\frac {1}{2} \sin (2 y(x))}{x (x+1)} \] ✓ Mathematica : cpu = 0.605085 (sec), leaf count = 43
DSolve[Derivative[1][y][x] == (x^4/2 + (x^4*Cos[2*y[x]])/2 - Sin[2*y[x]]/2 - (x*Sin[2*y[x]])/2)/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {3 x^4-4 x^3+6 x^2-12 x+12 \log (x+1)-25-12 c_1}{12 x}\right )\right \}\right \}\] ✓ Maple : cpu = 1.323 (sec), leaf count = 38
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))*x-sin(2*y(x))+cos(2*y(x))*x^4+x^4)/x/(1+x),y(x))
\[y \left (x \right ) = \arctan \left (\frac {3 x^{4}-4 x^{3}+6 x^{2}+12 \ln \left (1+x \right )-12 c_{1}-12 x}{12 x}\right )\]