\[ y'(x)=\frac {1}{2} e^{-\frac {x^2}{2}} y(x) \left (2 e^{\frac {x^2}{4}} y(x)+2 e^{\frac {x^2}{2}}+e^{\frac {x^2}{2}} x+2 y(x)^2\right ) \] ✓ Mathematica : cpu = 0.354312 (sec), leaf count = 132
\[\text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\& ,\frac {\log \left (\frac {3 e^{-\frac {x^2}{2}} y(x)+e^{-\frac {x^2}{4}}}{\sqrt [3]{7} \sqrt [3]{-e^{-\frac {3 x^2}{4}}}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 7^{2/3} e^{\frac {x^2}{2}} \left (-e^{-\frac {3 x^2}{4}}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 1.261 (sec), leaf count = 145
\[ \left \{ -{\frac {2}{3}\ln \left ( -6+ \left ( 18\,y \left ( x \right ) {{\rm e}^{-1/2\,{x}^{2}}}+6\,{{\rm e}^{-1/4\,{x}^{2}}} \right ) {{\rm e}^{{\frac {{x}^{2}}{4}}}} \right ) }+{\frac {1}{3}\ln \left ( 36+{\frac {324}{7} \left ( y \left ( x \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}+{\frac {1}{3}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {{x}^{2}}{4}}}} \right ) ^{2}}+{\frac {1}{7} \left ( 108\,y \left ( x \right ) {{\rm e}^{-1/2\,{x}^{2}}}+36\,{{\rm e}^{-1/4\,{x}^{2}}} \right ) {{\rm e}^{{\frac {{x}^{2}}{4}}}}} \right ) }+{\frac {2\,\sqrt {3}}{9}\arctan \left ( {\frac {\sqrt {3}}{9} \left ( 6\,y \left ( x \right ) {{\rm e}^{-1/2\,{x}^{2}}}+2\,{{\rm e}^{-1/4\,{x}^{2}}} \right ) {{\rm e}^{{\frac {{x}^{2}}{4}}}}}+{\frac {\sqrt {3}}{9}} \right ) }+{\frac {2\,x}{3}}-{\it \_C1}=0 \right \} \]