\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{a}^{2}x+{a}^{3}{x}^{3}+{a}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}+2\,{a}^{2}{x}^{2}y \left ( x \right ) +ax+ \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}{x}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}{x}^{2}+3\,axy \left ( x \right ) +1}{{a}^{3}{x}^{3}}}=0} \]
Mathematica: cpu = 0.060508 (sec), leaf count = 85 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {a x+3}{a x}+3 y(x)}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 46 \[ \left \{ y \left ( x \right ) ={\frac {29\,{\it RootOf} \left ( -81\, \int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) ax-3\,ax-9}{9\,ax}} \right \} \]