\[ y'(x)=\frac {-\frac {1}{32} x^3 y(x)^3+\frac {1}{16} x^2 y(x)^3+\frac {3}{16} x^2 y(x)^2-\frac {1}{2} x y(x)^3+\frac {y(x)^3}{4}-\frac {1}{4} x y(x)^2-\frac {3}{8} x y(x)+\frac {y(x)}{4}+\frac {1}{4}}{x y(x)} \] ✓ Mathematica : cpu = 0.757207 (sec), leaf count = 683
\[\text {Solve}\left [\int _1^{y(x)}\left (-32 \text {RootSum}\left [\text {$\#$1}^3 K[1]^3-2 \text {$\#$1}^2 K[1]^3-8 K[1]^3-6 \text {$\#$1}^2 K[1]^2+8 \text {$\#$1} K[1]^2+12 \text {$\#$1} K[1]-8 K[1]-8\& ,\frac {\log (x-\text {$\#$1})}{3 \text {$\#$1}^2 K[1]^2-4 \text {$\#$1} K[1]^2-12 \text {$\#$1} K[1]+8 K[1]+12}\& \right ] K[1]+\frac {32 K[1]}{x^3 K[1]^3-2 x^2 K[1]^3-8 K[1]^3-6 x^2 K[1]^2+8 x K[1]^2+12 x K[1]-8 K[1]-8}-\frac {8 \text {RootSum}\left [\text {$\#$1}^3 K[1]^3-2 \text {$\#$1}^2 K[1]^3-8 K[1]^3-6 \text {$\#$1}^2 K[1]^2+8 \text {$\#$1} K[1]^2+12 \text {$\#$1} K[1]-8 K[1]-8\& ,\frac {-x \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+20 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+12 x \log (x-\text {$\#$1}) K[1]^3+8 \log (x-\text {$\#$1}) K[1]^3-18 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^3-12 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^3+2 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^2+\text {$\#$1}^2 K[1]^2+36 x \log (x-\text {$\#$1}) K[1]^2+4 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^2-44 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^2+18 \text {$\#$1} K[1]^2-12 K[1]^2-4 x \log (x-\text {$\#$1}) K[1]+8 \log (x-\text {$\#$1}) K[1]-8 \log (x-\text {$\#$1}) \text {$\#$1} K[1]-4 \text {$\#$1} K[1]-36 K[1]+8 \log (x-\text {$\#$1})+4}{x \text {$\#$1}^2 K[1]^3-20 \text {$\#$1}^2 K[1]^3+112 x K[1]^3+18 x \text {$\#$1} K[1]^3-112 \text {$\#$1} K[1]^3-8 K[1]^3-2 \text {$\#$1}^2 K[1]^2-36 x K[1]^2-4 x \text {$\#$1} K[1]^2+44 \text {$\#$1} K[1]^2+4 x K[1]+8 \text {$\#$1} K[1]-8 K[1]-8}\& \right ]}{K[1]}\right )dK[1]+16 y(x)^2 \text {RootSum}\left [\text {$\#$1}^3 y(x)^3-2 \text {$\#$1}^2 y(x)^3-6 \text {$\#$1}^2 y(x)^2+8 \text {$\#$1} y(x)^2+12 \text {$\#$1} y(x)-8 y(x)^3-8 y(x)-8\& ,\frac {\log (x-\text {$\#$1})}{3 \text {$\#$1}^2 y(x)^2-4 \text {$\#$1} y(x)^2-12 \text {$\#$1} y(x)+8 y(x)+12}\& \right ]+\log (x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.037 (sec), leaf count = 42
\[y \relax (x ) = \frac {18}{58 \RootOf \left (-324 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \relax (x )+12 c_{1}\right )+9 x -6}\]