#### 2.801   ODE No. 801

$y'(x)=\frac {1}{2} e^{\frac {x^2}{4}} \left (2 e^{-\frac {3 x^2}{4}} y(x)^3+2 e^{-\frac {x^2}{2}} y(x)^2+e^{-\frac {x^2}{4}} x y(x)+2\right )$ Mathematica : cpu = 0.361924 (sec), leaf count = 126

$\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {\#1}^3+3 \sqrt [3]{29} \text {\#1}-29\& ,\frac {\log \left (\frac {3 e^{-\frac {x^2}{2}} y(x)+e^{-\frac {x^2}{4}}}{\sqrt [3]{29} \sqrt [3]{e^{-\frac {3 x^2}{4}}}}-\text {\#1}\right )}{\sqrt [3]{29}-29 \text {\#1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} e^{\frac {x^2}{2}} \left (e^{-\frac {3 x^2}{4}}\right )^{2/3} x,y(x)\right ]$ Maple : cpu = 0.043 (sec), leaf count = 63

$\left \{ y \left ( x \right ) ={\frac {1}{9} \left ( -3\,{{\rm e}^{-1/4\,{x}^{2}}}{{\rm e}^{1/4\,{x}^{2}}}+29\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) \right ) \left ( {{\rm e}^{{\frac {{x}^{2}}{4}}}} \right ) ^{-1} \left ( {{\rm e}^{-{\frac {{x}^{2}}{2}}}} \right ) ^{-1}} \right \}$