\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{\it \_F1} \left ( \left ( y \left ( x \right ) \right ) ^{2}-2\,\ln \left ( x \right ) \right ) }{\sqrt { \left ( y \left ( x \right ) \right ) ^{2}}x}}=0} \]
Mathematica: cpu = 0.080010 (sec), leaf count = 386 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (\frac {4 K[2] \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^3 \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2-1\right ){}^2}+\frac {4 \sqrt {K[2]^2} \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2 \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2-1\right ){}^2}-\frac {4 K[2] \text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right ) \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2-1\right )}-\frac {2 \sqrt {K[2]^2} \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2-1\right )}\right ) \, dK[1]+\frac {K[2]}{\left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )\right ){}^2-1}+\frac {\sqrt {K[2]^2} \text {$\_$F1}\left (K[2]^2-2 \log (x)\right )}{\left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )\right ){}^2-1}\right ) \, dK[2]+\int _1^x \left (-\frac {\left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )\right ){}^2-1\right )}-\frac {\sqrt {y(x)^2} \text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )}{y(x) K[1] \left (\left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )\right ){}^2-1\right )}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.327 (sec), leaf count = 65 \[ \left \{ y \left ( x \right ) =\sqrt {2\,\ln \left ( x \right ) +2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) },y \left ( x \right ) =-\sqrt {2\,\ln \left ( x \right ) + 2\,{\it RootOf} \left ( \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( {\it \_F1} \left ( 2\,{\it \_a} \right ) -1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) } \right \} \]