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