\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( \left ( {{\rm e}^{-1/4\,{x}^{2}}} \right ) ^{2}xy \left ( x \right ) +{{\rm e}^{-1/4\,{x}^{2}}}x+2\, \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{-3/4\,{x}^{2}}} \right ) {{\rm e}^{1/4\,{x}^{2}}}}{2\,y \left ( x \right ) {{\rm e}^{-1/4\,{x}^{2}}}+2}}=0} \]
Mathematica: cpu = 0.041005 (sec), leaf count = 137 \[ \left \{\left \{y(x)\to \frac {2 e^{\frac {x^2}{2}}}{\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}} \left (c_1-2 x\right )+2 e^{\frac {x^2}{2}}}-2 e^{\frac {x^2}{4}}}\right \},\left \{y(x)\to -\frac {2 e^{\frac {x^2}{2}}}{\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}} \left (c_1-2 x\right )+2 e^{\frac {x^2}{2}}}+2 e^{\frac {x^2}{4}}}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 186 \[ \left \{ y \left ( x \right ) ={1 \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}} }}\sqrt {{\it \_C1}-2\,x}{{\rm e}^{{\frac {{x}^{2}}{2}}}}-{{\rm e}^{-{ \frac {{x}^{2}}{4}}}}{{\rm e}^{{\frac {{x}^{2}}{2}}}}-{{\rm e}^{{ \frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x} \right ) \left ( {{\rm e}^ {-{\frac {{x}^{2}}{4}}}} \right ) ^{-1} \left ( {{\rm e}^{-{\frac {{x}^{ 2}}{4}}}}{{\rm e}^{{\frac {{x}^{2}}{2}}}}+{{\rm e}^{{\frac {{x}^{2}}{4 }}}}\sqrt {{\it \_C1}-2\,x} \right ) ^{-1}},y \left ( x \right ) =-{1 \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x}{ {\rm e}^{{\frac {{x}^{2}}{2}}}}+{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{ {\rm e}^{{\frac {{x}^{2}}{2}}}}-{{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1}-2\,x} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1} \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}}{{\rm e}^{{ \frac {{x}^{2}}{2}}}}-{{\rm e}^{{\frac {{x}^{2}}{4}}}}\sqrt {{\it \_C1 }-2\,x} \right ) ^{-1}} \right \} \]