\[ y(x) \left (a f(x)^2-\frac {f''(x)}{f(x)}+3 f'(x)+\frac {3 f'(x)^2}{f(x)^2}\right )+b f(x)^3-\left (\frac {f'(x)}{f(x)}+f(x)\right ) \left (3 y'(x)+y(x)^2\right )+y''(x)+y(x) y'(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 0.747487 (sec), leaf count = 0
, could not solve
DSolve[b*f[x]^3 - y[x]^3 + y[x]*Derivative[1][y][x] - (f[x] + Derivative[1][f][x]/f[x])*(y[x]^2 + 3*Derivative[1][y][x]) + y[x]*(a*f[x]^2 + 3*Derivative[1][f][x] + (3*Derivative[1][f][x]^2)/f[x]^2 - Derivative[2][f][x]/f[x]) + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \left (f \left (\RootOf \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}-\left (\int _{}^{\textit {\_Z}}f \left (\textit {\_f} \right )d \textit {\_f} \right )\right )\right ) \textit {\_a} \right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (-\textit {\_a}^{3}-\textit {\_a}^{2}+a \textit {\_a} +b \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (\textit {\_a} -3\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =\frac {y \relax (x )}{f \relax (x )}, \textit {\_}b\left (\textit {\_a} \right )=-\frac {f \relax (x )^{3}}{\left (\frac {d}{d x}f \relax (x )\right ) y \relax (x )-f \relax (x ) \left (\frac {d}{d x}y \relax (x )\right )}\right \}, \left \{x =\RootOf \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}-\left (\int _{}^{\textit {\_Z}}f \left (\textit {\_f} \right )d \textit {\_f} \right )\right ), y \relax (x )=f \left (\RootOf \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}-\left (\int _{}^{\textit {\_Z}}f \left (\textit {\_f} \right )d \textit {\_f} \right )\right )\right ) \textit {\_a} \right \}\right ]\]