\[ y'(x)=\frac {\frac {1}{2} x^3 \cos (2 y(x))+\frac {x^3}{2}-\frac {1}{2} \sin (2 y(x))}{x} \] ✓ Mathematica : cpu = 0.286483 (sec), leaf count = 21
DSolve[Derivative[1][y][x] == (x^3/2 + (x^3*Cos[2*y[x]])/2 - Sin[2*y[x]]/2)/x,y[x],x]
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {x^4+2 c_1}{4 x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.831 (sec), leaf count = 17
dsolve(diff(y(x),x) = 1/2*(-sin(2*y(x))+cos(2*y(x))*x^3+x^3)/x,y(x))
\[y \left (x \right ) = \arctan \left (\frac {x^{4}+8 c_{1}}{4 x}\right )\]