\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)^2-2 x\right )+x}{x \sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 1.52031 (sec), leaf count = 102
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {\sqrt {K[2]^2}}{\text {$\_$F1}\left (K[2]^2-2 x\right )}-\int _1^x \frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 K[1]\right )}{\left (\text {$\_$F1}\left (K[2]^2-2 K[1]\right )\right ){}^2} \, dK[1]\right ) \, dK[2]+\int _1^x \left (-\frac {1}{\text {$\_$F1}\left (y(x)^2-2 K[1]\right )}-\frac {1}{K[1]}\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.32 (sec), leaf count = 63
\[ \left \{ y \left ( x \right ) =\sqrt {2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) +2\,x},y \left ( x \right ) =-\sqrt {2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) +2\,x} \right \} \]