\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)+\frac {1}{x}\right )+\frac {1}{x}}{x} \] ✓ Mathematica : cpu = 0.121438 (sec), leaf count = 101
\[\text {Solve}\left [\int _1^{y(x)}-\frac {\text {$\_$F1}\left (K[2]+\frac {1}{x}\right ) \int _1^x-\frac {\text {$\_$F1}'\left (K[2]+\frac {1}{K[1]}\right )}{K[1]^2 \left (\text {$\_$F1}\left (K[2]+\frac {1}{K[1]}\right )\right ){}^2}dK[1]+1}{\text {$\_$F1}\left (K[2]+\frac {1}{x}\right )}dK[2]+\int _1^x\left (\frac {1}{K[1]}+\frac {1}{\text {$\_$F1}\left (y(x)+\frac {1}{K[1]}\right ) K[1]^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.249 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) x-1}{x}} \right \} \]