\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)+\frac {1}{x}\right )+\frac {1}{x}}{x} \] ✓ Mathematica : cpu = 0.140421 (sec), leaf count = 101
DSolve[Derivative[1][y][x] == (x^(-1) + _F1[x^(-1) + y[x]])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {\text {$\_$F1}\left (K[2]+\frac {1}{x}\right ) \int _1^x-\frac {\text {$\_$F1}'\left (K[2]+\frac {1}{K[1]}\right )}{K[1]^2 \left (\text {$\_$F1}\left (K[2]+\frac {1}{K[1]}\right )\right ){}^2}dK[1]+1}{\text {$\_$F1}\left (K[2]+\frac {1}{x}\right )}dK[2]+\int _1^x\left (\frac {1}{K[1]}+\frac {1}{\text {$\_$F1}\left (y(x)+\frac {1}{K[1]}\right ) K[1]^2}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.135 (sec), leaf count = 27
dsolve(diff(y(x),x) = -(-1/x-_F1(y(x)+1/x))/x,y(x))
\[y \left (x \right ) = \frac {\RootOf \left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right ) x -1}{x}\]