\[ y'(x)=\frac {\frac {1}{2} x^2 \cos (2 y(x))+\frac {x^2}{2}-\frac {1}{2} \sin (2 y(x))}{x} \] ✓ Mathematica : cpu = 0.304625 (sec), leaf count = 23
DSolve[Derivative[1][y][x] == (x^2/2 + (x^2*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {2 x^3+3 c_1}{6 x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.56 (sec), leaf count = 17
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+cos(2*y(x))*x^2+x^2)/x,y(x))
\[y \left (x \right ) = \arctan \left (\frac {x^{3}+6 c_{1}}{3 x}\right )\]