#### 2.606   ODE No. 606

$y'(x)=-x \left (-F\left (y(x)-\frac {1}{2} e^{-x^2} x^2\right )+e^{-x^2} x^2-e^{-x^2}\right )$ Mathematica : cpu = 0.567191 (sec), leaf count = 361

$\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right ) \int _1^x\left (\frac {e^{-K[1]^2} F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]^3}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}-\frac {e^{-K[1]^2} \left (e^{K[1]^2} F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right ) F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}+\frac {F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right )dK[1]+1}{F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right )}dK[2]+\int _1^x\left (\frac {e^{-K[1]^2} \left (e^{K[1]^2} F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right ) K[1]}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}-\frac {e^{-K[1]^2} K[1]^3}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.759 (sec), leaf count = 34

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