\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {y \left ( x \right ) \left ( 2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,y \left ( x \right ) {{\rm e}^{1/4\,{x}^{2}}}+2\, \left ( {{\rm e}^{1/4\,{x}^{2}}} \right ) ^{2}+x \left ( {{\rm e}^{1/4\,{x}^{2}}} \right ) ^{2} \right ) }{ \left ( {{\rm e}^{1/4\,{x}^{2}}} \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.104513 (sec), leaf count = 132 \[ \text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\& ,\frac {\log \left (\frac {3 e^{-\frac {x^2}{2}} y(x)+e^{-\frac {x^2}{4}}}{\sqrt [3]{7} \sqrt [3]{-e^{-\frac {3 x^2}{4}}}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 7^{2/3} e^{\frac {x^2}{2}} \left (-e^{-\frac {3 x^2}{4}}\right )^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.312 (sec), leaf count = 187 \[ \left \{ -{\frac {2}{3}\ln \left ( 18\,y \left ( x \right ) {{\rm e}^{-1 /2\,{x}^{2}}}{{\rm e}^{1/4\,{x}^{2}}}+6\,{{\rm e}^{-1/4\,{x}^{2}}}{ {\rm e}^{1/4\,{x}^{2}}}-6 \right ) }+{\frac {1}{3}\ln \left ( {\frac { 324\, \left ( y \left ( x \right ) \right ) ^{2}}{7} \left ( {{\rm e}^{-{ \frac {{x}^{2}}{2}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {{x}^{2}}{4 }}}} \right ) ^{2}}+{\frac {216\,y \left ( x \right ) }{7}{{\rm e}^{-{ \frac {{x}^{2}}{2}}}} \left ( {{\rm e}^{{\frac {{x}^{2}}{4}}}} \right ) ^{2}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}}+{\frac {36}{7} \left ( {{\rm e}^ {-{\frac {{x}^{2}}{4}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {{x}^{2} }{4}}}} \right ) ^{2}}+{\frac {108\,y \left ( x \right ) }{7}{{\rm e}^{{ \frac {{x}^{2}}{4}}}}{{\rm e}^{-{\frac {{x}^{2}}{2}}}}}+{\frac {36}{7} {{\rm e}^{-{\frac {{x}^{2}}{4}}}}{{\rm e}^{{\frac {{x}^{2}}{4}}}}}+36 \right ) }+{\frac {2\,\sqrt {3}}{9}\arctan \left ( {\frac {\sqrt {3}}{9 } \left ( 6\,y \left ( x \right ) {{\rm e}^{-1/2\,{x}^{2}}}{{\rm e}^{1/4 \,{x}^{2}}}+2\,{{\rm e}^{-1/4\,{x}^{2}}}{{\rm e}^{1/4\,{x}^{2}}}+1 \right ) } \right ) }+{\frac {2\,x}{3}}-{\it \_C1}=0 \right \} \]