\[ y'(x)=\frac {x^3 y(x)^3+x^3 y(x)^2+x^3+6 x^2 y(x)^2+4 x^2 y(x)+12 x y(x)+6 x+8}{x^3} \] ✓ Mathematica : cpu = 0.178968 (sec), leaf count = 80
DSolve[Derivative[1][y][x] == (8 + 6*x + x^3 + 12*x*y[x] + 4*x^2*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^2 + x^3*y[x]^3)/x^3,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 y(x)+\frac {x+6}{x}}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.024 (sec), leaf count = 41
dsolve(diff(y(x),x) = (6*x+x^3+x^3*y(x)^2+4*x^2*y(x)+x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8)/x^3,y(x))
\[y \left (x \right ) = \frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right ) x -3 x -18}{9 x}\]