\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{\frac {y \left ( x \right ) -xf \left ( {x}^{2}+a \left ( y \left ( x \right ) \right ) ^{2} \right ) }{x+ay \left ( x \right ) f \left ( {x}^{2}+a \left ( y \left ( x \right ) \right ) ^{2} \right ) }}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.312 (sec), leaf count = 52 \[ \left \{ {1\arctan \left ( {x\sqrt {a}{\frac {1}{\sqrt {{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) {\frac {1}{\sqrt {a}}}}-{ \frac {1}{2}\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{\frac {{x }^{2}}{a}}}\!{\frac {f \left ( {\it \_a}\,a \right ) }{{\it \_a}}}{d{ \it \_a}}}-{\it \_C1}=0 \right \} \]