\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac {1}{x} \left ( -{x}^{-1}-{\it \_F1} \left ( y \left ( x \right ) +{x}^{-1} \right ) \right ) }=0} \]
Mathematica: cpu = 0.075510 (sec), leaf count = 98 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {\text {$\_$F1}\left (K[2]+\frac {1}{x}\right ) \left (\int _1^x -\frac {\text {$\_$F1}'\left (K[2]+\frac {1}{K[1]}\right )}{K[1]^2 \left (\text {$\_$F1}\left (K[2]+\frac {1}{K[1]}\right )\right ){}^2} \, dK[1]\right )+1}{\text {$\_$F1}\left (K[2]+\frac {1}{x}\right )} \, dK[2]+\int _1^x \left (\frac {1}{K[1]^2 \text {$\_$F1}\left (\frac {1}{K[1]}+y(x)\right )}+\frac {1}{K[1]}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.125 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) x-1}{x}} \right \} \]