\[ y'(x)=\frac {(y(x) \log (x)-1)^3}{x (-y(x)+y(x) \log (x)-1)} \] ✓ Mathematica : cpu = 1.24108 (sec), leaf count = 546
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {\log (x) K[1]-K[1]-1}{\log ^3(x) K[1]^3+\log (x) K[1]^3-K[1]^3-3 \log ^2(x) K[1]^2-K[1]^2+3 \log (x) K[1]-1}+\text {RootSum}\left [K[1]^3-\text {$\#$1} K[1]^2-\text {$\#$1}^3\& ,\frac {K[1] \log (K[1] \log (x)-\text {$\#$1}-1)-\log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}}{K[1]^2+3 \text {$\#$1}^2}\& \right ]+\frac {\text {RootSum}\left [K[1]^3-\text {$\#$1} K[1]^2-\text {$\#$1}^3\& ,\frac {4 \log (x) K[1]^3-4 \log (x) \log (K[1] \log (x)-\text {$\#$1}-1) K[1]^3-12 \log (K[1] \log (x)-\text {$\#$1}-1) K[1]^3+12 K[1]^3+4 \log (K[1] \log (x)-\text {$\#$1}-1) K[1]^2+5 \log (x) \text {$\#$1} K[1]^2-5 \log (x) \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]^2+16 \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]^2-16 \text {$\#$1} K[1]^2-12 \log (x) \text {$\#$1}^2 K[1]+12 \log (x) \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2 K[1]+5 \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2 K[1]-5 \text {$\#$1}^2 K[1]+5 \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]-12 \log (K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2}{28 \log (x) K[1]^3-9 K[1]^3-27 \log (x) \text {$\#$1} K[1]^2-19 \text {$\#$1} K[1]^2-28 K[1]^2+9 \log (x) \text {$\#$1}^2 K[1]+27 \text {$\#$1}^2 K[1]+27 \text {$\#$1} K[1]-9 \text {$\#$1}^2}\& \right ]}{K[1]}\right )dK[1]-y(x) \text {RootSum}\left [-\text {$\#$1}^3-\text {$\#$1} y(x)^2+y(x)^3\& ,\frac {y(x) \log (-\text {$\#$1}+y(x) \log (x)-1)-\text {$\#$1} \log (-\text {$\#$1}+y(x) \log (x)-1)}{3 \text {$\#$1}^2+y(x)^2}\& \right ]-\log (x)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.09 (sec), leaf count = 78
\[y \relax (x ) = \frac {47 \RootOf \left (-27783 \left (\int _{}^{\textit {\_Z}}\frac {1}{2209 \textit {\_a}^{3}-9261 \textit {\_a} +9261}d \textit {\_a} \right )-7 \ln \relax (x )+3 c_{1}\right )-84}{\left (47 \ln \relax (x )-47\right ) \RootOf \left (-27783 \left (\int _{}^{\textit {\_Z}}\frac {1}{2209 \textit {\_a}^{3}-9261 \textit {\_a} +9261}d \textit {\_a} \right )-7 \ln \relax (x )+3 c_{1}\right )-84 \ln \relax (x )+21}\]