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 = 0.109689 (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 = 0.162 (sec), leaf count = 173

\[\left \{y \left (x \right ) = -\frac {2^{\frac {2}{3}} \sqrt {-240 \left (\left (-\frac {3 \Gamma \left (\frac {2}{3}\right ) \Gamma \left (\frac {1}{3}, -2 x^{3}\right )}{2}+\pi \sqrt {3}\right ) x \,{\mathrm e}^{-2 x^{3}}+\frac {9 \left (-\frac {3 c_{1} {\mathrm e}^{-2 x^{3}}}{2}+x \right ) 2^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}}{40}\right ) 2^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )}, y \left (x \right ) = \frac {2^{\frac {2}{3}} \sqrt {-240 \left (\left (-\frac {3 \Gamma \left (\frac {2}{3}\right ) \Gamma \left (\frac {1}{3}, -2 x^{3}\right )}{2}+\pi \sqrt {3}\right ) x \,{\mathrm e}^{-2 x^{3}}+\frac {9 \left (-\frac {3 c_{1} {\mathrm e}^{-2 x^{3}}}{2}+x \right ) 2^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}}{40}\right ) 2^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )}\right \}\]