\[ \boxed { x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) -a{x}^{3}=0} \]
Mathematica: cpu = 0.018502 (sec), leaf count = 36 \[ \left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\frac {1}{2} \left (2 \sqrt {a} c_1+\sqrt {a} x^2\right )\right )\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 24 \[ \left \{ y \left ( x \right ) =\tanh \left ( {\frac {{x}^{2}}{2}\sqrt {a} }+{\it \_C1}\,\sqrt {a} \right ) x\sqrt {a} \right \} \]