\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac { \left( 3+y \left( x \right)  \right) ^{3}{{\rm e}^{9/2\,{x}^{2}}}x{{\rm e}^{3/2\,{x}^{2}}}}{ \left( 243\,{{\rm e}^{3/2\,{x}^{2}}}+81\,{{\rm e}^{3/2\,{x}^{2}}}y \left( x \right) +243\,y \left( x \right)  \right) {{\rm e}^{3\,{x}^{2}}}}}=0}
\]