\[ y'(x)=-\frac {x \left (-\text {$\_$F1}\left (y(x)^2-2 x\right )-\frac {1}{x}\right )}{\sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 0.617005 (sec), leaf count = 103
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {$\_$F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 K[1]\right )}{\left (\text {$\_$F1}\left (K[2]^2-2 K[1]\right )\right ){}^2}dK[1]\right )dK[2]+\int _1^x\left (-K[1]-\frac {1}{\text {$\_$F1}\left (y(x)^2-2 K[1]\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.533 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) =\sqrt {2\,{\it RootOf} \left ( {x}^{2}-2\,\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+4\,{\it \_C1} \right ) +2\,x},y \left ( x \right ) =-\sqrt {2\,{\it RootOf} \left ( {x}^{2}-2\,\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+4\,{\it \_C1} \right ) +2\,x} \right \} \]