\[ a x^2+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.123503 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\sqrt {-a x^2+c_1 x}\right \},\left \{y(x)\to \sqrt {-a x^2+c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.017 (sec), leaf count = 33
\[\left \{y \left (x \right ) = \sqrt {-a \,x^{2}+c_{1} x}, y \left (x \right ) = -\sqrt {-a \,x^{2}+c_{1} x}\right \}\]