2.1831   ODE No. 1831

\[ y(x) (x F(0,2)+x F(2,0)) y''(x)+x F(2,2) y''(x)^2+x F(1,1) y''(x)+y'(x) \left ((x F(1,2)+x F(2,1)) y''(x)+y(x) (x F(0,1)+x F(1,0))\right )+x F(0,0) y(x)^2=0 \] Mathematica : cpu = 71.5522 (sec), leaf count = 0


, could not solve

DSolve[x*F[0, 0]*y[x]^2 + x*F[1, 1]*Derivative[2][y][x] + (x*F[0, 2] + x*F[2, 0])*y[x]*Derivative[2][y][x] + x*F[2, 2]*Derivative[2][y][x]^2 + Derivative[1][y][x]*((x*F[0, 1] + x*F[1, 0])*y[x] + (x*F[1, 2] + x*F[2, 1])*Derivative[2][y][x]) == 0, y[x], x]

Maple : cpu = 0. (sec), leaf count = 0


, result contains DESol or ODESolStruc

\[y \relax (x ) = \left ({\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 )=-\textit {\_}b\left (\textit {\_a} \right )^{2}-\frac {\left (F_{2,1}\left (\textit {\_a} \right )+F_{1,2}\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )}{2 F_{2,2}\left (\textit {\_a} \right )}-\frac {F_{2,0}\left (\textit {\_a} \right )+F_{0,2}\left (\textit {\_a} \right )-\sqrt {F_{2,0}\left (\textit {\_a} \right )^{2}+2 F_{2,0}\left (\textit {\_a} \right ) F_{0,2}\left (\textit {\_a} \right )+2 F_{2,1}\left (\textit {\_a} \right ) F_{2,0}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )+2 F_{1,2}\left (\textit {\_a} \right ) F_{2,0}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )+F_{0,2}\left (\textit {\_a} \right )^{2}+2 F_{2,1}\left (\textit {\_a} \right ) F_{0,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )+2 F_{1,2}\left (\textit {\_a} \right ) F_{0,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )-4 F_{0,0}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right )+F_{2,1}\left (\textit {\_a} \right )^{2} \textit {\_}b\left (\textit {\_a} \right )^{2}+2 F_{2,1}\left (\textit {\_a} \right ) F_{1,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{2}+F_{1,2}\left (\textit {\_a} \right )^{2} \textit {\_}b\left (\textit {\_a} \right )^{2}-4 F_{1,0}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )-4 F_{0,1}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )-4 F_{1,1}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}}{2 F_{2,2}\left (\textit {\_a} \right )}\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=\frac {\frac {d}{d x}y \relax (x )}{y \relax (x )}\right \}, \left \{x =\textit {\_a} , y \relax (x )={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right \}\right ]\]