\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/9\,{\frac {x \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{3\,{x}^{2}}}}{{{\rm e}^{9/2\,{x}^{2}}}}F \left ( 1/3\,{\frac { \left ( 3+y \left ( x \right ) \right ) {{\rm e}^{3/2\,{x}^{2}}}}{y \left ( x \right ) }} \right ) }=0} \]
Mathematica: cpu = 67.610585 (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 = 0.234 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) =-3\,{\frac {{{\rm e}^{3/2\,{x}^{2}}}}{{ {\rm e}^{3/2\,{x}^{2}}}-3\,{\it RootOf} \left ( -{x}^{2}-18\,\int ^{{ \it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -27\,{\it \_a} \right ) ^ {-1}{d{\it \_a}}+2\,{\it \_C1} \right ) }} \right \} \]