\[ y'(x)=\frac {1}{-\left (x^2 \left (\frac {1}{y(x)}+1\right ) \text {$\_$F1}\left (x \left (\frac {1}{y(x)}+1\right )\right )\right )+x^2 \text {$\_$F1}\left (x \left (\frac {1}{y(x)}+1\right )\right )+x \left (\frac {1}{y(x)}+1\right )-x} \] ✓ Mathematica : cpu = 0.776136 (sec), leaf count = 365
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {x \text {$\_$F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )-1}{x \text {$\_$F1}\left (x \left (1+\frac {1}{K[2]}\right )\right ) K[2]-K[2]+x \text {$\_$F1}\left (x \left (1+\frac {1}{K[2]}\right )\right )}-\int _1^x\left (\frac {\text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {$\_$F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {$\_$F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}}{K[1] \left (K[2] \text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]}-\frac {\left (K[2] \text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right ) \left (K[1] \left (\text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )-\frac {K[1] \text {$\_$F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]}-\frac {K[1] \text {$\_$F1}'\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )}{K[2]^2}\right )-1\right )}{\left (K[1] \left (K[2] \text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )+\text {$\_$F1}\left (K[1] \left (1+\frac {1}{K[2]}\right )\right )\right )-K[2]\right ){}^2}\right )dK[1]\right )dK[2]+\int _1^x\left (\frac {y(x) \text {$\_$F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {$\_$F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )}{K[1] \left (y(x) \text {$\_$F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )+\text {$\_$F1}\left (K[1] \left (1+\frac {1}{y(x)}\right )\right )\right )-y(x)}-\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.223 (sec), leaf count = 40
\[y \relax (x ) = {\mathrm e}^{\RootOf \left (-\textit {\_Z} -\left (\int _{}^{\frac {x \,{\mathrm e}^{\textit {\_Z}}}{{\mathrm e}^{\textit {\_Z}}-1}}\frac {1}{\left (\textit {\_F1} \left (\textit {\_a} \right ) \textit {\_a} -1\right ) \textit {\_a}}d \textit {\_a} \right )+c_{1}\right )}-1\]