\[ x \left (\sqrt {x y(x)}-1\right ) y'(x)-y(x) \left (\sqrt {x y(x)}+1\right )=0 \] ✓ Mathematica : cpu = 0.345587 (sec), leaf count = 34
\[\text {Solve}\left [\log (y(x))-\frac {y(x) \log (x)-\frac {2 y(x)}{\sqrt {x y(x)}}}{y(x)}=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.017 (sec), leaf count = 33
\[\left \{-\frac {1+\left (c_{1}-\ln \left (x \right )+\frac {\ln \left (x y \left (x \right )\right )}{2}\right ) \sqrt {x y \left (x \right )}}{\sqrt {x y \left (x \right )}} = 0\right \}\]