#### 2.686   ODE No. 686

$y'(x)=\frac {e^{2 x^2} x y(x)^3}{e^{x^2} y(x)+1}$ Mathematica : cpu = 11.7191 (sec), leaf count = 68

$\text {Solve}\left [\log (y(x))-2 y(x)^2 \left (\frac {\log \left (e^{2 x^2} y(x)^2+2 e^{x^2} y(x)+2\right )}{4 y(x)^2}-\frac {\tan ^{-1}\left (e^{x^2} y(x)+1\right )}{2 y(x)^2}\right )=c_1,y(x)\right ]$ Maple : cpu = 0.098 (sec), leaf count = 85

$\left \{ y \left ( x \right ) ={\frac {1}{{{\rm e}^{{x}^{2}}}} \left ( 1-\tan \left ( {\it RootOf} \left ( -2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) \right ) \left ( \tan \left ( {\it RootOf} \left ( -2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) \right ) ^{-1}} \right \}$