\[ y'(x)=\frac {e^{\frac {x^2}{4}} y(x) \left (2 e^{-\frac {3 x^2}{4}} y(x)^2+e^{-\frac {x^2}{2}} x y(x)+e^{-\frac {x^2}{4}} x\right )}{2 e^{-\frac {x^2}{4}} y(x)+2} \] ✓ Mathematica : cpu = 0.32708 (sec), leaf count = 137
DSolve[Derivative[1][y][x] == (E^(x^2/4)*y[x]*(x/E^(x^2/4) + (x*y[x])/E^(x^2/2) + (2*y[x]^2)/E^((3*x^2)/4)))/(2 + (2*y[x])/E^(x^2/4)),y[x],x]
\[\left \{\left \{y(x)\to \frac {2 e^{\frac {x^2}{2}}}{-2 e^{\frac {x^2}{4}}+\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}}+2 e^{\frac {x^2}{2}} (-2 x+c_1)}}\right \},\left \{y(x)\to -\frac {2 e^{\frac {x^2}{2}}}{2 e^{\frac {x^2}{4}}+\sqrt {2} \sqrt {2 e^{\frac {x^2}{2}}+2 e^{\frac {x^2}{2}} (-2 x+c_1)}}\right \}\right \}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 162
dsolve(diff(y(x),x) = y(x)*(exp(-1/4*x^2)^2*x*y(x)+exp(-1/4*x^2)*x+2*y(x)^2*exp(-3/4*x^2))*exp(1/4*x^2)/(2*y(x)*exp(-1/4*x^2)+2),y(x))
\[y \left (x \right ) = \frac {\left ({\mathrm e}^{\frac {x^{2}}{2}} \left (\sqrt {c_{1}-2 x}+1\right ) {\mathrm e}^{-\frac {x^{2}}{4}}-{\mathrm e}^{\frac {x^{2}}{4}} \sqrt {c_{1}-2 x}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{{\mathrm e}^{\frac {x^{2}}{4}} \sqrt {c_{1}-2 x}-{\mathrm e}^{-\frac {x^{2}}{4}} {\mathrm e}^{\frac {x^{2}}{2}}}\]