2.1719   ODE No. 1719

\[ a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0 \] Mathematica : cpu = 41.8062 (sec), leaf count = 0


, could not solve

DSolve[g[x]*y[x]^2 + f[x]*y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]

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


, result contains DESol or ODESolStruc

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