#### 2.617   ODE No. 617

$y'(x)=\frac {1}{9} e^{-\frac {3 x^2}{2}} x y(x)^2 F\left (\frac {e^{\frac {3 x^2}{2}} (y(x)+3)}{3 y(x)}\right )$ Mathematica : cpu = 0.950582 (sec), leaf count = 615

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {9 e^{\frac {3 x^2}{2}}-F\left (\frac {e^{\frac {3 x^2}{2}} (K[2]+3)}{3 K[2]}\right )}{3 \left (\left (9 e^{\frac {3 x^2}{2}}-F\left (\frac {e^{\frac {3 x^2}{2}} (K[2]+3)}{3 K[2]}\right )\right ) K[2]+27 e^{\frac {3 x^2}{2}}\right )}-\int _1^x\left (-\frac {K[2] \left (\frac {e^{\frac {3 K[1]^2}{2}}}{3 K[2]}-\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]^2}\right ) F'\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[1]}{-9 e^{\frac {3 K[1]^2}{2}} K[2]+F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[2]-27 e^{\frac {3 K[1]^2}{2}}}+\frac {F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[2] \left (F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )-9 e^{\frac {3 K[1]^2}{2}}+K[2] \left (\frac {e^{\frac {3 K[1]^2}{2}}}{3 K[2]}-\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]^2}\right ) F'\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right )\right ) K[1]}{\left (-9 e^{\frac {3 K[1]^2}{2}} K[2]+F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[2]-27 e^{\frac {3 K[1]^2}{2}}\right )^2}-\frac {F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[1]}{-9 e^{\frac {3 K[1]^2}{2}} K[2]+F\left (\frac {e^{\frac {3 K[1]^2}{2}} (K[2]+3)}{3 K[2]}\right ) K[2]-27 e^{\frac {3 K[1]^2}{2}}}\right )dK[1]-\frac {1}{3 K[2]}\right )dK[2]+\int _1^x-\frac {F\left (\frac {e^{\frac {3 K[1]^2}{2}} (y(x)+3)}{3 y(x)}\right ) K[1] y(x)}{-9 e^{\frac {3 K[1]^2}{2}} y(x)+F\left (\frac {e^{\frac {3 K[1]^2}{2}} (y(x)+3)}{3 y(x)}\right ) y(x)-27 e^{\frac {3 K[1]^2}{2}}}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.527 (sec), leaf count = 47

$\left \{ y \left ( x \right ) =-3\,{\frac {{{\rm e}^{3/2\,{x}^{2}}}}{{{\rm e}^{3/2\,{x}^{2}}}-3\,{\it RootOf} \left ( -{x}^{2}-18\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -27\,{\it \_a} \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) }} \right \}$