\[ y'(x)=\frac {1}{9} e^{-\frac {3 x^2}{2}} x y(x)^2 F\left (\frac {e^{\frac {3 x^2}{2}} (y(x)+3)}{3 y(x)}\right ) \] ✓ Mathematica : cpu = 273.855 (sec), leaf count = 612
\[\text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (-\frac {K[2] \left (\frac {e^{\frac {3 K[1]^2}{2}}}{3 K[2]}-\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]^2}\right ) K[1] F'\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )}{K[2] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}} K[2]-27 e^{\frac {3 K[1]^2}{2}}}+\frac {K[2] K[1] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) \left (K[2] \left (\frac {e^{\frac {3 K[1]^2}{2}}}{3 K[2]}-\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]^2}\right ) F'\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )+F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}}\right )}{\left (K[2] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}} K[2]-27 e^{\frac {3 K[1]^2}{2}}\right )^2}-\frac {K[1] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )}{K[2] F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}} K[2]-27 e^{\frac {3 K[1]^2}{2}}}\right ) \, dK[1]+\frac {9 e^{\frac {3 x^2}{2}}-F\left (\frac {e^{\frac {3 x^2}{2}} (K[2]+3)}{3 K[2]}\right )}{3 \left (K[2] \left (9 e^{\frac {3 x^2}{2}}-F\left (\frac {e^{\frac {3 x^2}{2}} (K[2]+3)}{3 K[2]}\right )\right )+27 e^{\frac {3 x^2}{2}}\right )}-\frac {1}{3 K[2]}\right ) \, dK[2]+\int _1^x -\frac {y(x) K[1] F\left (\frac {(y(x)+3) e^{\frac {3 K[1]^2}{2}}}{3 y(x)}\right )}{y(x) F\left (\frac {(y(x)+3) e^{\frac {3 K[1]^2}{2}}}{3 y(x)}\right )-9 y(x) e^{\frac {3 K[1]^2}{2}}-27 e^{\frac {3 K[1]^2}{2}}} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.296 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) =-3\,{\frac {{{\rm e}^{3/2\,{x}^{2}}}}{{{\rm e}^{3/2\,{x}^{2}}}-3\,{\it RootOf} \left ( -{x}^{2}-18\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -27\,{\it \_a} \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) }} \right \} \]