#### 2.263   ODE No. 263

$2 x^3+3 x^2 y(x)^2+y(x) y'(x)+7=0$ Mathematica : cpu = 0.0901645 (sec), leaf count = 181

$\left \{\left \{y(x)\to -\sqrt {c_1 e^{-2 x^3}+\frac {7\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}-\frac {2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {4}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}}\right \},\left \{y(x)\to \sqrt {c_1 e^{-2 x^3}+\frac {7\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}-\frac {2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {4}{3},-2 x^3\right )}{3 \sqrt [3]{-x^3}}}\right \}\right \}$ Maple : cpu = 0.106 (sec), leaf count = 173

$\left \{ y \left ( x \right ) =-{\frac {{2}^{{\frac {2}{3}}}}{18\,\Gamma \left ( 2/3 \right ) }\sqrt {-240\,\sqrt [3]{-{x}^{3}} \left ( {\frac { \left ( -{\frac {27\,{{\rm e}^{-2\,{x}^{3}}}{\it \_C1}}{2}}+9\,x \right ) \sqrt [3]{2}\Gamma \left ( 2/3 \right ) \sqrt [3]{-{x}^{3}}}{40}}+{{\rm e}^{-2\,{x}^{3}}}x \left ( \pi \,\sqrt {3}-3/2\,\Gamma \left ( 1/3,-2\,{x}^{3} \right ) \Gamma \left ( 2/3 \right ) \right ) \right ) \sqrt [3]{2}\Gamma \left ( 2/3 \right ) }{\frac {1}{\sqrt [3]{-{x}^{3}}}}},y \left ( x \right ) ={\frac {{2}^{{\frac {2}{3}}}}{18\,\Gamma \left ( 2/3 \right ) }\sqrt {-240\,\sqrt [3]{-{x}^{3}} \left ( {\frac { \left ( -{\frac {27\,{{\rm e}^{-2\,{x}^{3}}}{\it \_C1}}{2}}+9\,x \right ) \sqrt [3]{2}\Gamma \left ( 2/3 \right ) \sqrt [3]{-{x}^{3}}}{40}}+{{\rm e}^{-2\,{x}^{3}}}x \left ( \pi \,\sqrt {3}-3/2\,\Gamma \left ( 1/3,-2\,{x}^{3} \right ) \Gamma \left ( 2/3 \right ) \right ) \right ) \sqrt [3]{2}\Gamma \left ( 2/3 \right ) }{\frac {1}{\sqrt [3]{-{x}^{3}}}}} \right \}$