\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ax \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) =0} \]
Mathematica: cpu = 0.034004 (sec), leaf count = 31 \[ \left \{\left \{y(x)\to -\frac {e^{c_1}}{a e^{c_1}-\sqrt {x^2-1}}\right \}\right \} \]
Maple: cpu = 0.0 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) = \left ( \sqrt {x-1}\sqrt {1+x}{\it \_C1}- a \right ) ^{-1} \right \} \]