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