\[ y'(x)=\frac {a^3 x^3 y(x)^3+a^3 x^3 y(x)^2+a^3 x^3+3 a^2 x^2 y(x)^2+2 a^2 x^2 y(x)+a^2 x+3 a x y(x)+a x+1}{a^3 x^3} \] ✓ Mathematica : cpu = 0.243453 (sec), leaf count = 85
DSolve[Derivative[1][y][x] == (1 + a*x + a^2*x + a^3*x^3 + 3*a*x*y[x] + 2*a^2*x^2*y[x] + 3*a^2*x^2*y[x]^2 + a^3*x^3*y[x]^2 + a^3*x^3*y[x]^3)/(a^3*x^3),y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {a x+3}{a x}+3 y(x)}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.037 (sec), leaf count = 46
dsolve(diff(y(x),x) = (a^2*x+a^3*x^3+a^3*x^3*y(x)^2+2*a^2*x^2*y(x)+a*x+y(x)^3*a^3*x^3+3*y(x)^2*a^2*x^2+3*a*x*y(x)+1)/a^3/x^3,y(x))
\[y \left (x \right ) = \frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right ) a x -3 a x -9}{9 a x}\]