\[ y'(x)=\frac {\text {$\_$F1}\left (y(x)^2-2 \log (x)\right )}{x \sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 0.245365 (sec), leaf count = 637
DSolve[Derivative[1][y][x] == _F1[-2*Log[x] + y[x]^2]/(x*Sqrt[y[x]^2]),y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{\left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )+1\right )}-\int _1^x\left (\frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ){}^2 \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )\right ){}^2}{K[1] \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+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 (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 \sqrt {K[2]^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 (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ){}^2 \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}+\frac {2 \sqrt {K[2]^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 (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+1\right ){}^2}-\frac {2 \sqrt {K[2]^2} \text {$\_$F1}'\left (K[2]^2-2 \log (K[1])\right )}{K[1] \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (K[1])\right )+1\right )}\right )dK[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 )-1\right ) \left (\text {$\_$F1}\left (K[2]^2-2 \log (x)\right )+1\right )}\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 (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )+1\right )}-\frac {\sqrt {y(x)^2} \text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )}{K[1] y(x) \left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )-1\right ) \left (\text {$\_$F1}\left (y(x)^2-2 \log (K[1])\right )+1\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.471 (sec), leaf count = 65
dsolve(diff(y(x),x) = _F1(y(x)^2-2*ln(x))/(y(x)^2)^(1/2)/x,y(x))
\[y \left (x \right ) = \sqrt {2 \ln \left (x \right )+2 \operatorname {RootOf}\left (\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )-1}d \textit {\_a} \right )+c_{1}\right )}\]