\[ y'(x)=\frac {\csc \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{x}\right ) \left (x^4 \sin \left (\frac {y(x)}{2 x}\right ) \sin \left (\frac {y(x)}{x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+x^3 \sin \left (\frac {y(x)}{2 x}\right ) \sin \left (\frac {y(x)}{x}\right ) \cos \left (\frac {y(x)}{2 x}\right )-\frac {1}{2} y(x) \sin \left (\frac {y(x)}{x}\right )+x \sin \left (\frac {y(x)}{2 x}\right ) \sin \left (\frac {y(x)}{x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {3 y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )\right )}{x} \] ✓ Mathematica : cpu = 0.278253 (sec), leaf count = 29
DSolve[Derivative[1][y][x] == (Csc[y[x]/(2*x)]*Sec[y[x]/(2*x)]*Sec[y[x]/x]*(x*Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)]*Sin[y[x]/x] + x^3*Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)]*Sin[y[x]/x] + x^4*Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)]*Sin[y[x]/x] + (Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)]*y[x])/2 - (Sin[y[x]/x]*y[x])/2 + (Cos[y[x]/(2*x)]*Sin[(3*y[x])/(2*x)]*y[x])/2))/x,y[x],x]
\[\left \{\left \{y(x)\to x \sin ^{-1}\left (x e^{\frac {x^3}{3}+\frac {x^2}{2}+c_1}\right )\right \}\right \}\] ✓ Maple : cpu = 0.069 (sec), leaf count = 26
dsolve(diff(y(x),x) = 1/2*(-y(x)*sin(y(x)/x)+y(x)*sin(3/2*y(x)/x)*cos(1/2*y(x)/x)+y(x)*cos(1/2*y(x)/x)*sin(1/2*y(x)/x)+2*sin(y(x)/x)*cos(1/2*y(x)/x)*sin(1/2*y(x)/x)*x+2*sin(y(x)/x)*x^3*cos(1/2*y(x)/x)*sin(1/2*y(x)/x)+2*sin(y(x)/x)*x^4*cos(1/2*y(x)/x)*sin(1/2*y(x)/x))/cos(y(x)/x)/cos(1/2*y(x)/x)/sin(1/2*y(x)/x)/x,y(x))
\[y \left (x \right ) = \arcsin \left (x \,{\mathrm e}^{\frac {x^{3}}{3}} {\mathrm e}^{\frac {x^{2}}{2}} c_{1}\right ) x\]