\[ y'(x)=\frac {y(x)^3+y(x)+y(x)^3 \left (-\log ^3(x)\right )+y(x)^3 \log ^2(x)+3 y(x)^2 \log ^2(x)-2 y(x)^2 \log (x)-3 y(x) \log (x)+1}{x y(x)} \] ✓ Mathematica : cpu = 0.758696 (sec), leaf count = 716
\[\text {Solve}\left [\int _1^{y(x)}\left (2 \text {RootSum}\left [\text {$\#$1}^3 K[1]^3-\text {$\#$1}^2 K[1]^3-2 K[1]^3-3 \text {$\#$1}^2 K[1]^2+2 \text {$\#$1} K[1]^2+3 \text {$\#$1} K[1]-K[1]-1\& ,\frac {\log (\log (x)-\text {$\#$1})}{3 \text {$\#$1}^2 K[1]^2-2 \text {$\#$1} K[1]^2-6 \text {$\#$1} K[1]+2 K[1]+3}\& \right ] K[1]-\frac {K[1]}{\log ^3(x) K[1]^3-\log ^2(x) K[1]^3-2 K[1]^3-3 \log ^2(x) K[1]^2+2 \log (x) K[1]^2+3 \log (x) K[1]-K[1]-1}+\frac {\text {RootSum}\left [\text {$\#$1}^3 K[1]^3-\text {$\#$1}^2 K[1]^3-2 K[1]^3-3 \text {$\#$1}^2 K[1]^2+2 \text {$\#$1} K[1]^2+3 \text {$\#$1} K[1]-K[1]-1\& ,\frac {-2 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+38 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^3+12 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^3+4 \log (\log (x)-\text {$\#$1}) K[1]^3-36 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3-12 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^3+2 \log (\log (x)-\text {$\#$1}) \text {$\#$1}^2 K[1]^2+\text {$\#$1}^2 K[1]^2+36 \log (x) \log (\log (x)-\text {$\#$1}) K[1]^2+4 \log (x) \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2-40 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]^2+18 \text {$\#$1} K[1]^2-6 K[1]^2-2 \log (x) \log (\log (x)-\text {$\#$1}) K[1]+2 \log (\log (x)-\text {$\#$1}) K[1]-4 \log (\log (x)-\text {$\#$1}) \text {$\#$1} K[1]-2 \text {$\#$1} K[1]-18 K[1]+2 \log (\log (x)-\text {$\#$1})+1}{\log (x) \text {$\#$1}^2 K[1]^3-19 \text {$\#$1}^2 K[1]^3+110 \log (x) K[1]^3+18 \log (x) \text {$\#$1} K[1]^3-110 \text {$\#$1} K[1]^3-2 K[1]^3-\text {$\#$1}^2 K[1]^2-18 \log (x) K[1]^2-2 \log (x) \text {$\#$1} K[1]^2+20 \text {$\#$1} K[1]^2+\log (x) K[1]+2 \text {$\#$1} K[1]-K[1]-1}\& \right ]}{K[1]}\right )dK[1]+y(x)^2 \left (-\text {RootSum}\left [\text {$\#$1}^3 y(x)^3-\text {$\#$1}^2 y(x)^3-3 \text {$\#$1}^2 y(x)^2+2 \text {$\#$1} y(x)^2+3 \text {$\#$1} y(x)-2 y(x)^3-y(x)-1\& ,\frac {\log (\log (x)-\text {$\#$1})}{3 \text {$\#$1}^2 y(x)^2-2 \text {$\#$1} y(x)^2-6 \text {$\#$1} y(x)+2 y(x)+3}\& \right ]\right )-\log (x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.189 (sec), leaf count = 43
\[y \relax (x ) = \frac {9}{9 \ln \relax (x )+56 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{3136 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )-\ln \relax (x )+3 c_{1}\right )-3}\]