\[ a x+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.0949386 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\sqrt {-a x \log (x)+c_1 x}\right \},\left \{y(x)\to \sqrt {-a x \log (x)+c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.018 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) =\sqrt {-ax\ln \left ( x \right ) +{\it \_C1}\,x},y \left ( x \right ) =-\sqrt {-x \left ( a\ln \left ( x \right ) -{\it \_C1} \right ) } \right \} \]