\[ y'(x)=\frac {\csc \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{x}\right ) \left (x^4 \sin \left (\frac {y(x)}{2 x}\right ) \sin \left (\frac {y(x)}{x}\right ) \cos \left (\frac {y(x)}{2 x}\right )-\frac {1}{2} x y(x) \sin \left (\frac {y(x)}{x}\right )-\frac {1}{2} y(x) \sin \left (\frac {y(x)}{x}\right )+\frac {1}{2} x y(x) \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} x y(x) \sin \left (\frac {3 y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {3 y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )\right )}{x (x+1)} \] ✓ Mathematica : cpu = 0.266431 (sec), leaf count = 30
DSolve[Derivative[1][y][x] == (Csc[y[x]/(2*x)]*Sec[y[x]/(2*x)]*Sec[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 + (x*Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)]*y[x])/2 - (Sin[y[x]/x]*y[x])/2 - (x*Sin[y[x]/x]*y[x])/2 + (Cos[y[x]/(2*x)]*Sin[(3*y[x])/(2*x)]*y[x])/2 + (x*Cos[y[x]/(2*x)]*Sin[(3*y[x])/(2*x)]*y[x])/2))/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to x \arcsin \left ((x+1) e^{\frac {x^2}{2}-x-\frac {3}{2}+c_1}\right )\right \}\right \}\] ✓ Maple : cpu = 0.328 (sec), leaf count = 29
dsolve(diff(y(x),x) = 1/2*(-sin(y(x)/x)*y(x)*x-y(x)*sin(y(x)/x)+y(x)*sin(3/2*y(x)/x)*cos(1/2*y(x)/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)*x+y(x)*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/(1+x),y(x))
\[y \left (x \right ) = \frac {\arccos \left (\left (c_{1} \left (1+x \right )^{2} {\mathrm e}^{x^{2}}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}\right ) x}{2}\]