#### 2.620   ODE No. 620

$y'(x)=\frac {e^{2 F(-(x-y(x)) (y(x)+x))}+x^2+2 x y(x)+y(x)^2}{-e^{2 F(-(x-y(x)) (y(x)+x))}+x^2+2 x y(x)+y(x)^2}$ Mathematica : cpu = 0.762136 (sec), leaf count = 210

$\text {Solve}\left [\int _1^{y(x)}\left (-\frac {2 K[2]}{-x^2+e^{2 F(-(x-K[2]) (x+K[2]))}+K[2]^2}-\int _1^x\left (\frac {2 K[1] \left (-4 \exp (2 F(-(K[1]-K[2]) (K[1]+K[2]))) F'(-(K[1]-K[2]) (K[1]+K[2])) K[2]-2 K[2]\right )}{\left (K[1]^2-\exp (2 F(-(K[1]-K[2]) (K[1]+K[2])))-K[2]^2\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 K[1]}{K[1]^2-\exp (2 F(-(K[1]-y(x)) (K[1]+y(x))))-y(x)^2}\right )dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.492 (sec), leaf count = 37

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