2.1682   ODE No. 1682

\[ x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0 \] Mathematica : cpu = 21.7398 (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 = 0. (sec), leaf count = 0


, result contains DESol or ODESolStruc

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