2.263   ODE No. 263

$3 x^2 y(x)^2+2 x^3+y(x) y'(x)+7=0$ Mathematica : cpu = 0.0851859 (sec), leaf count = 181

$\left \{\left \{y(x)\to -\sqrt {\frac {7\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}-\frac {2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {4}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}+c_1 e^{-2 x^3}}\right \},\left \{y(x)\to \sqrt {\frac {7\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}-\frac {2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {4}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}+c_1 e^{-2 x^3}}\right \}\right \}$ Maple : cpu = 0.115 (sec), leaf count = 179

$\left \{ y \left ( x \right ) =-{\frac {{2}^{{\frac {2}{3}}}\sqrt {3}}{18\,\Gamma \left ( 2/3 \right ) }\sqrt {-80\,\Gamma \left ( 2/3 \right ) \sqrt [3]{2}\sqrt [3]{-{x}^{3}} \left ( {\frac {9\,\Gamma \left ( 2/3 \right ) \sqrt [3]{2} \left ( -3/2\,{{\rm e}^{-2\,{x}^{3}}}{\it \_C1}+x \right ) \sqrt [3]{-{x}^{3}}}{40}}+{{\rm e}^{-2\,{x}^{3}}}x \left ( \pi \,\sqrt {3}-3/2\,\Gamma \left ( 1/3,-2\,{x}^{3} \right ) \Gamma \left ( 2/3 \right ) \right ) \right ) }{\frac {1}{\sqrt [3]{-{x}^{3}}}}},y \left ( x \right ) ={\frac {{2}^{{\frac {2}{3}}}\sqrt {3}}{18\,\Gamma \left ( 2/3 \right ) }\sqrt {-80\,\Gamma \left ( 2/3 \right ) \sqrt [3]{2}\sqrt [3]{-{x}^{3}} \left ( {\frac {9\,\Gamma \left ( 2/3 \right ) \sqrt [3]{2} \left ( -3/2\,{{\rm e}^{-2\,{x}^{3}}}{\it \_C1}+x \right ) \sqrt [3]{-{x}^{3}}}{40}}+{{\rm e}^{-2\,{x}^{3}}}x \left ( \pi \,\sqrt {3}-3/2\,\Gamma \left ( 1/3,-2\,{x}^{3} \right ) \Gamma \left ( 2/3 \right ) \right ) \right ) }{\frac {1}{\sqrt [3]{-{x}^{3}}}}} \right \}$