\[ a x+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.132447 (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 = 0.029 (sec), leaf count = 34
\[\left \{y \left (x \right ) = \sqrt {-a x \ln \left (x \right )+c_{1} x}, y \left (x \right ) = -\sqrt {-\left (a \ln \left (x \right )-c_{1}\right ) x}\right \}\]