\[ y'(x)=\frac {\csc (y(x)) \left (\frac {1}{2} x^3 \log (x) \cos (2 y(x))+\frac {1}{2} x^3 \log (x)-\cos (y(x))\right )}{x \log (x)} \] ✓ Mathematica : cpu = 0.594891 (sec), leaf count = 63
DSolve[Derivative[1][y][x] == (Csc[y[x]]*(-Cos[y[x]] + (x^3*Log[x])/2 + (x^3*Cos[2*y[x]]*Log[x])/2))/(x*Log[x]),y[x],x]
\[\left \{\left \{y(x)\to -\sec ^{-1}\left (\frac {-x^3+3 x^3 \log (x)-9 c_1}{9 \log (x)}\right )\right \},\left \{y(x)\to \sec ^{-1}\left (\frac {-x^3+3 x^3 \log (x)-9 c_1}{9 \log (x)}\right )\right \}\right \}\] ✓ Maple : cpu = 0.97 (sec), leaf count = 27
dsolve(diff(y(x),x) = 1/2*(-2*cos(y(x))+x^3*cos(2*y(x))*ln(x)+x^3*ln(x))/sin(y(x))/ln(x)/x,y(x))
\[y \left (x \right ) = \arccos \left (\frac {9 \ln \left (x \right )}{3 x^{3} \ln \left (x \right )-x^{3}+9 c_{1}}\right )\]