\[ y'(x)=\frac {y(x)^3+y(x)-8 y(x)^3 \log ^3(x)+4 y(x)^3 \log ^2(x)+12 y(x)^2 \log ^2(x)-4 y(x)^2 \log (x)-6 y(x) \log (x)+1}{x y(x)} \] ✓ Mathematica : cpu = 0.829654 (sec), leaf count = 724
\[\text {Solve}\left [\int _1^{y(x)}\left (4 \text {RootSum}\left [8 \text {$\#$1}^3 K[1]^3-4 \text {$\#$1}^2 K[1]^3-3 K[1]^3-12 \text {$\#$1}^2 K[1]^2+4 \text {$\#$1} K[1]^2+6 \text {$\#$1} K[1]-K[1]-1\& ,\frac {\log (\log (x)-\text {$\#$1})}{12 \text {$\#$1}^2 K[1]^2-4 \text {$\#$1} K[1]^2-12 \text {$\#$1} K[1]+2 K[1]+3}\& \right ] K[1]-\frac {2 K[1]}{8 \log ^3(x) K[1]^3-4 \log ^2(x) K[1]^3-3 K[1]^3-12 \log ^2(x) K[1]^2+4 \log (x) K[1]^2+6 \log (x) K[1]-K[1]-1}-\frac {2 \text {RootSum}\left [8 \text {$\#$1}^3 K[1]^3-4 \text {$\#$1}^2 K[1]^3-3 K[1]^3-12 \text {$\#$1}^2 K[1]^2+4 \text {$\#$1} K[1]^2+6 \text {$\#$1} K[1]-K[1]-1\& ,\frac {16 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3-224 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3-36 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^3-6 \log (\log (x)-\text {$\#$1}) K[1]^3+216 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3+36 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3-8 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^2-4 \text {$\#$1}^2 K[1]^2-108 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^2-16 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2+116 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2-54 \text {$\#$1} K[1]^2+9 K[1]^2+4 \log (x) \log (\log (x)-\text {$\#$1}) K[1]-2 \log (\log (x)-\text {$\#$1}) K[1]+8 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]+4 \text {$\#$1} K[1]+27 K[1]-2 \log (\log (x)-\text {$\#$1})-1}{8 \log (x) \text {$\#$1}^2 K[1]^3-112 \text {$\#$1}^2 K[1]^3+492 \log (x) K[1]^3+108 \log (x) \text {$\#$1} K[1]^3-492 \text {$\#$1} K[1]^3-3 K[1]^3-4 \text {$\#$1}^2 K[1]^2-54 \log (x) K[1]^2-8 \log (x) \text {$\#$1} K[1]^2+58 \text {$\#$1} K[1]^2+2 \log (x) K[1]+4 \text {$\#$1} K[1]-K[1]-1}\& \right ]}{K[1]}\right )dK[1]-2 \left (y(x)^2 \text {RootSum}\left [8 \text {$\#$1}^3 y(x)^3-4 \text {$\#$1}^2 y(x)^3-12 \text {$\#$1}^2 y(x)^2+4 \text {$\#$1} y(x)^2+6 \text {$\#$1} y(x)-3 y(x)^3-y(x)-1\& ,\frac {\log (\log (x)-\text {$\#$1})}{12 \text {$\#$1}^2 y(x)^2-4 \text {$\#$1} y(x)^2-12 \text {$\#$1} y(x)+2 y(x)+3}\& \right ]+\log (x)\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.083 (sec), leaf count = 43
\[y \relax (x ) = \frac {9}{18 \ln \relax (x )+83 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{6889 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \relax (x )+3 c_{1}\right )-3}\]