2.1682   ODE No. 1682

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

\[ x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0 \] Mathematica : cpu = 22.2405 (sec), leaf count = 41

\[\left \{\left \{y(x)\to \frac {2+x^3 \wp '(x+c_1;0,c_2)}{x \left (-1+x^2 \wp (x+c_1;0,c_2)\right )}\right \}\right \}\] Maple : cpu = 1.964 (sec), leaf count = 94

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=-\left (\textit {\_a} +\left (\textit {\_a}^{3}+\textit {\_a}^{2}-14 \textit {\_a} -24\right ) \textit {\_}b\left (\textit {\_a} \right )-3\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =x y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=-\frac {1}{\left (x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )\right ) x}\right \}, \left \{x ={\mathrm e}^{-c_{1}+\int -\textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]