\[ x \left (\sqrt {x y(x)}-1\right ) y'(x)-y(x) \left (\sqrt {x y(x)}+1\right )=0 \] ✓ Mathematica : cpu = 0.18656 (sec), leaf count = 29
DSolve[-(y[x]*(1 + Sqrt[x*y[x]])) + x*(-1 + Sqrt[x*y[x]])*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {2}{\sqrt {x y(x)}}+2 \log (y(x))-\log (x y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.011 (sec), leaf count = 33
dsolve(((x*y(x))^(1/2)-1)*x*diff(y(x),x)-((x*y(x))^(1/2)+1)*y(x) = 0,y(x))
\[-\frac {1+\left (c_{1}-\ln \left (x \right )+\frac {\ln \left (x y \left (x \right )\right )}{2}\right ) \sqrt {x y \left (x \right )}}{\sqrt {x y \left (x \right )}} = 0\]