\[ y'(x)=\frac {1}{9} e^{-\frac {3 x^2}{2}} x y(x)^2 F\left (\frac {e^{\frac {3 x^2}{2}} (y(x)+3)}{3 y(x)}\right ) \] ✓ Mathematica : cpu = 270.631 (sec), leaf count = 302
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {9 e^{\frac {3 K[1]^2}{2}} K[1] \left (e^{\frac {3 K[1]^2}{2}} (K[2]+3) F'\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-3 K[2] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )\right )}{K[2] \left (K[2] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}} (K[2]+3)\right )^2} \, dK[1]-\frac {9 e^{\frac {3 x^2}{2}}}{K[2] \left (9 e^{\frac {3 x^2}{2}} (K[2]+3)-K[2] F\left (\frac {e^{\frac {3 x^2}{2}} (K[2]+3)}{3 K[2]}\right )\right )}\right ) \, dK[2]+\int _1^x -\frac {y(x) K[1] F\left (\frac {(y(x)+3) e^{\frac {3 K[1]^2}{2}}}{3 y(x)}\right )}{y(x) \left (F\left (\frac {(y(x)+3) e^{\frac {3 K[1]^2}{2}}}{3 y(x)}\right )-9 e^{\frac {3 K[1]^2}{2}}\right )-27 e^{\frac {3 K[1]^2}{2}}} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 1.109 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) =-3\,{\frac {{{\rm e}^{3/2\,{x}^{2}}}}{{{\rm e}^{3/2\,{x}^{2}}}-3\,{\it RootOf} \left ( -{x}^{2}-18\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -27\,{\it \_a} \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) }} \right \} \]