\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)+\frac {1}{x}\right )+\frac {1}{x}}{x} \] ✓ Mathematica : cpu = 0.0829548 (sec), leaf count = 88
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {\text {$\_$F1}'\left (K[2]+\frac {1}{K[1]}\right )}{K[1]^2 \left (\text {$\_$F1}\left (K[2]+\frac {1}{K[1]}\right )\right ){}^2} \, dK[1]-\frac {1}{\text {$\_$F1}\left (K[2]+\frac {1}{x}\right )}\right ) \, dK[2]+\int _1^x \frac {\frac {1}{\text {$\_$F1}\left (\frac {1}{K[1]}+y(x)\right )}+K[1]}{K[1]^2} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.147 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) x-1}{x}} \right \} \]