\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =1/2\,{\frac {1}{x \left( 1+x \right) } \left( y \left( x \right) \sin \left( 3/2\,{\frac {y \left( x \right) }{x}} \right) \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) x+y \left( x \right) \sin \left( 3/2\,{\frac {y \left( x \right) }{x}} \right) \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) +y \left( x \right) \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) \sin \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) x+y \left( x \right) \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) \sin \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) -\sin \left( {\frac {y \left( x \right) }{x}} \right) y \left( x \right) x-y \left( x \right) \sin \left( {\frac {y \left( x \right) }{x}} \right) +2\,\sin \left( {\frac {y \left( x \right) }{x}} \right) \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) \sin \left( 1/2\,{\frac {y \left( x \right) }{x}} \right) x \right)  \left( \cos \left( {\frac {y \left( x \right) }{x}} \right)  \right) ^{-1} \left( \cos \left( 1/2\,{\frac {y \left( x \right) }{x}} \right)  \right) ^{-1} \left( \sin \left( 1/2\,{\frac {y \left( x \right) }{x}} \right)  \right) ^{-1}}=0}
\]