#### 2.815   ODE No. 815

$y'(x)=\frac {e^{3 x^2} x (y(x)+3)^3}{81 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )}$ Mathematica : cpu = 12.9188 (sec), leaf count = 99

$\text {Solve}\left [\frac {1}{186} \left (\left (31+3 \sqrt {93}\right ) \log \left (9 \left (9+\sqrt {93}\right ) y(x)-2 e^{\frac {3 x^2}{2}} (y(x)+3)\right )+\left (31-3 \sqrt {93}\right ) \log \left (2 e^{\frac {3 x^2}{2}} (y(x)+3)+9 \left (\sqrt {93}-9\right ) y(x)\right )\right )-\frac {1}{3} \log (3 y(x)+9)=c_1,y(x)\right ]$ Maple : cpu = 0.604 (sec), leaf count = 168

$\left \{ -10\,\ln \left ( {\frac {10\,{{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) }{27\,{{\rm e}^{3/2\,{x}^{2}}}+9\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +27\,y \left ( x \right ) }} \right ) +5\,\ln \left ( {\frac {100\, \left ( 3+y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}+ \left ( -8100\, \left ( y \left ( x \right ) \right ) ^{2}-24300\,y \left ( x \right ) \right ) {{\rm e}^{3/2\,{x}^{2}}}-24300\, \left ( y \left ( x \right ) \right ) ^{2}}{189\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) +3\,y \left ( x \right ) \right ) ^{2}}} \right ) -{\frac {30\,\sqrt {93}}{31}{\it Artanh} \left ( {\sqrt {93} \left ( 29\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +87\,{{\rm e}^{3/2\,{x}^{2}}}+81\,y \left ( x \right ) \right ) \left ( \left ( 279\,y \left ( x \right ) +837 \right ) {{\rm e}^{{\frac {3\,{x}^{2}}{2}}}}+837\,y \left ( x \right ) \right ) ^{-1}} \right ) }+15\,{x}^{2}-{\it \_C1}=0 \right \}$