\[ y'(x)=\frac {x \left (12 e^{-x^2} x^2 y(x)^2+8 e^{-x^2} x^2 y(x)-8 e^{-x^2} y(x)+4 e^{-2 x^2} x^2+8 e^{-x^2} x^2-8 e^{-x^2}+e^{-3 x^2} x^6-6 e^{-2 x^2} x^4 y(x)-4 e^{-2 x^2} x^4-8 y(x)^3\right )}{4 e^{-x^2} x^2-8 y(x)-8} \] ✓ Mathematica : cpu = 0.63857 (sec), leaf count = 150
DSolve[Derivative[1][y][x] == (x*(-8/E^x^2 + (4*x^2)/E^(2*x^2) + (8*x^2)/E^x^2 - (4*x^4)/E^(2*x^2) + x^6/E^(3*x^2) - (8*y[x])/E^x^2 + (8*x^2*y[x])/E^x^2 - (6*x^4*y[x])/E^(2*x^2) + (12*x^2*y[x]^2)/E^x^2 - 8*y[x]^3))/(-8 + (4*x^2)/E^x^2 - 8*y[x]),y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-x^2} \left (2 e^{x^2}-x^2\right )+\frac {e^{-3 x^2}}{8 \left (\frac {1}{8} e^{-3 x^2}-\frac {e^{-3 x^2}}{\sqrt {-64 x^2+c_1}}\right )}\right \},\left \{y(x)\to -\frac {1}{2} e^{-x^2} \left (2 e^{x^2}-x^2\right )+\frac {e^{-3 x^2}}{8 \left (\frac {1}{8} e^{-3 x^2}+\frac {e^{-3 x^2}}{\sqrt {-64 x^2+c_1}}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.132 (sec), leaf count = 85
dsolve(diff(y(x),x) = (-8*exp(-x^2)*y(x)+4*x^2*exp(-x^2)^2-8*exp(-x^2)+8*x^2*exp(-x^2)*y(x)-4*x^4*exp(-x^2)^2+8*x^2*exp(-x^2)-8*y(x)^3+12*x^2*exp(-x^2)*y(x)^2-6*y(x)*x^4*exp(-x^2)^2+x^6*exp(-x^2)^3)*x/(-8*y(x)+4*x^2*exp(-x^2)-8),y(x))
\[y \left (x \right ) = \frac {2+x^{2} \left (\sqrt {-x^{2}+c_{1}}-1\right ) {\mathrm e}^{-x^{2}}}{2 \sqrt {-x^{2}+c_{1}}-2}\]