\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =1/2\,{\frac {y \left( x \right)  \left( 2\, \left( y \left( x \right)  \right) ^{2}+2\,y \left( x \right) {{\rm e}^{1/4\,{x}^{2}}}+2\, \left( {{\rm e}^{1/4\,{x}^{2}}} \right) ^{2}+x \left( {{\rm e}^{1/4\,{x}^{2}}} \right) ^{2} \right) }{ \left( {{\rm e}^{1/4\,{x}^{2}}} \right) ^{2}}}=0}
\]