2.263   ODE No. 263

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ 2 x^3+3 x^2 y(x)^2+y(x) y'(x)+7=0 \] Mathematica : cpu = 0.0436029 (sec), leaf count = 120

\[\left \{\left \{y(x)\to -\frac {1}{3} \sqrt {9 c_1 e^{-2 x^3}+\frac {20\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{\sqrt [3]{-x^3}}-6 x}\right \},\left \{y(x)\to \sqrt {c_1 e^{-2 x^3}+\frac {20\ 2^{2/3} e^{-2 x^3} x \Gamma \left (\frac {1}{3},-2 x^3\right )}{9 \sqrt [3]{-x^3}}-\frac {2 x}{3}}\right \}\right \}\]

Maple : cpu = 0.238 (sec), leaf count = 179

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