\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)^2-2 \log (x)\right )}{x \sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 0.118493 (sec), leaf count = 234
\[\text {Solve}\left [c_1=\int _1^{y(x)} \frac {-\left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )\right ){}^2-1\right ) \left (\int _1^x \frac {2 \left (\sqrt {K[2]^2} \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2+2 K[2] \text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+\sqrt {K[2]^2}\right ) \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2-1\right ){}^2} \, dK[1]\right )+\sqrt {K[2]^2} \text {$\_$F1}\left (K[2]^2-2 \log (x)\right )+K[2]}{\left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )\right ){}^2-1} \, dK[2]+\int _1^x -\frac {\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right ) \left (y(x) \text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )+\sqrt {y(x)^2}\right )}{y(x) K[1] \left (\left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )\right ){}^2-1\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.598 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) =\sqrt {2\,\ln \left ( x \right ) +2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {2\,\ln \left ( x \right ) +2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) } \right \} \]