\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)^2-2 x\right )+x}{x \sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 0.895476 (sec), leaf count = 105
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {$\_$F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 K[1]\right )}{\left (\text {$\_$F1}\left (K[2]^2-2 K[1]\right )\right ){}^2}dK[1]\right )dK[2]+\int _1^x\left (-\frac {1}{\text {$\_$F1}\left (y(x)^2-2 K[1]\right )}-\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.265 (sec), leaf count = 63
\[\left \{y \left (x \right ) = \sqrt {2 x +2 \RootOf \left (2 c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+\ln \left (x \right )\right )}, y \left (x \right ) = -\sqrt {2 x +2 \RootOf \left (2 c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+\ln \left (x \right )\right )}\right \}\]