\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) {a}^{2}x+a+{a}^{2}x+ \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}{x}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}{x}^{2}+3\,axy \left ( x \right ) +1}{{a}^{2}{x}^{2} \left ( axy \left ( x \right ) +1+ax \right ) }}=0} \]
Mathematica: cpu = 0.049006 (sec), leaf count = 106 \[ \left \{\left \{y(x)\to \frac {1}{a^3 x^3 \left (\frac {1}{a^3 x^3}-\frac {1}{x^3 \sqrt {c_1-2 a^6 x}}\right )}-\frac {a x+1}{a x}\right \},\left \{y(x)\to \frac {1}{a^3 x^3 \left (\frac {1}{x^3 \sqrt {c_1-2 a^6 x}}+\frac {1}{a^3 x^3}\right )}-\frac {a x+1}{a x}\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 70 \[ \left \{ y \left ( x \right ) =-{\frac {1}{ax} \left ( -ax+\sqrt {{\it \_C1}-2\,x}-1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) ^{-1}} ,y \left ( x \right ) =-{\frac {1}{ax} \left ( ax+\sqrt {{\it \_C1}-2\,x} +1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) ^{-1}} \right \} \]