\[ y'(x)=\frac {1}{2} e^{-\frac {x^2}{2}} y(x) \left (2 e^{\frac {x^2}{4}} y(x)+2 e^{\frac {x^2}{2}}+e^{\frac {x^2}{2}} x+2 y(x)^2\right ) \] ✓ Mathematica : cpu = 0.395083 (sec), leaf count = 132
DSolve[Derivative[1][y][x] == (y[x]*(2*E^(x^2/2) + E^(x^2/2)*x + 2*E^(x^2/4)*y[x] + 2*y[x]^2))/(2*E^(x^2/2)),y[x],x]
\[\text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\& ,\frac {\log \left (\frac {3 e^{-\frac {x^2}{2}} y(x)+e^{-\frac {x^2}{4}}}{\sqrt [3]{7} \sqrt [3]{-e^{-\frac {3 x^2}{4}}}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 7^{2/3} e^{\frac {x^2}{2}} \left (-e^{-\frac {3 x^2}{4}}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.287 (sec), leaf count = 145
dsolve(diff(y(x),x) = 1/2*y(x)/exp(1/4*x^2)^2*(2*y(x)^2+2*y(x)*exp(1/4*x^2)+2*exp(1/4*x^2)^2+x*exp(1/4*x^2)^2),y(x))
\[-\frac {2 \ln \left (-6+\left (18 y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{2}}+6 \,{\mathrm e}^{-\frac {x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}\right )}{3}+\frac {\ln \left (36+\frac {324 \left (y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{2}}+\frac {{\mathrm e}^{-\frac {x^{2}}{4}}}{3}\right )^{2} {\mathrm e}^{\frac {x^{2}}{2}}}{7}+\frac {\left (108 y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{2}}+36 \,{\mathrm e}^{-\frac {x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{7}\right )}{3}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\left (6 y \left (x \right ) {\mathrm e}^{-\frac {x^{2}}{2}}+2 \,{\mathrm e}^{-\frac {x^{2}}{4}}\right ) \sqrt {3}\, {\mathrm e}^{\frac {x^{2}}{4}}}{9}+\frac {\sqrt {3}}{9}\right )}{9}+\frac {2 x}{3}-c_{1} = 0\]