\[ \boxed { 2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}+a{x}^{2}=0} \]
Mathematica: cpu = 0.009001 (sec), leaf count = 41 \[ \left \{\left \{y(x)\to -\sqrt {c_1 x-a x^2}\right \},\left \{y(x)\to \sqrt {c_1 x-a x^2}\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) =\sqrt {-a{x}^{2}+{\it \_C1}\,x},y \left ( x \right ) =-\sqrt {-a{x}^{2}+{\it \_C1}\,x} \right \} \]