\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {1}{x} \left ( -y \left ( x \right ) \sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) +y \left ( x \right ) \sin \left ( 3/2\,{\frac {y \left ( x \right ) }{x}} \right ) \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) +y \left ( x \right ) \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) +2\,\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) x+2\,\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) {x}^{3}\cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) +2\,\sin \left ( {\frac {y \left ( x \right ) }{x}} \right ) {x}^{4}\cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) \left ( \cos \left ( {\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1} \left ( \cos \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1} \left ( \sin \left ( 1/2\,{\frac {y \left ( x \right ) }{x}} \right ) \right ) ^{-1}}=0} \]
Mathematica: cpu = 0.056007 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to x \sin ^{-1}\left (x e^{c_1+\frac {x^3}{3}+\frac {x^2}{2}}\right )\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\frac {x}{2}\arccos \left ( {{\rm e}^{{ \frac {2\,{x}^{3}}{3}}}}{{\rm e}^{{x}^{2}}}{\it \_C1}\,{x}^{2}+1 \right ) } \right \} \]