\[ y'(x)=\frac {1}{2} e^{\frac {x^2}{4}} \left (2 e^{-\frac {3 x^2}{4}} y(x)^3+2 e^{-\frac {x^2}{2}} y(x)^2+e^{-\frac {x^2}{4}} x y(x)+2\right ) \] ✓ Mathematica : cpu = 0.380032 (sec), leaf count = 126
DSolve[Derivative[1][y][x] == (E^(x^2/4)*(2 + (x*y[x])/E^(x^2/4) + (2*y[x]^2)/E^(x^2/2) + (2*y[x]^3)/E^((3*x^2)/4)))/2,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 e^{-\frac {x^2}{2}} y(x)+e^{-\frac {x^2}{4}}}{\sqrt [3]{29} \sqrt [3]{e^{-\frac {3 x^2}{4}}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} e^{\frac {x^2}{2}} \left (e^{-\frac {3 x^2}{4}}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.063 (sec), leaf count = 63
dsolve(diff(y(x),x) = 1/2*(y(x)*exp(-1/4*x^2)*x+2+2*y(x)^2*exp(-1/2*x^2)+2*y(x)^3*exp(-3/4*x^2))*exp(1/4*x^2),y(x))
\[y \left (x \right ) = \frac {\left (-3 \,{\mathrm e}^{-\frac {x^{2}}{4}} {\mathrm e}^{\frac {x^{2}}{4}}+29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )\right ) {\mathrm e}^{-\frac {x^{2}}{4}} {\mathrm e}^{\frac {x^{2}}{2}}}{9}\]