\[ y'(x)=\frac {(y(x) \log (x)-1)^3}{x (-y(x)+y(x) \log (x)-1)} \] ✓ Mathematica : cpu = 11.3678 (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 = 0.275 (sec), leaf count = 78
\[ \left \{ y \left ( x \right ) ={\frac {47\,{\it RootOf} \left ( -27783\,\int ^{{\it \_Z}}\! \left ( 2209\,{{\it \_a}}^{3}-9261\,{\it \_a}+9261 \right ) ^{-1}{d{\it \_a}}-7\,\ln \left ( x \right ) +3\,{\it \_C1} \right ) -84}{ \left ( 47\,\ln \left ( x \right ) -47 \right ) {\it RootOf} \left ( -27783\,\int ^{{\it \_Z}}\! \left ( 2209\,{{\it \_a}}^{3}-9261\,{\it \_a}+9261 \right ) ^{-1}{d{\it \_a}}-7\,\ln \left ( x \right ) +3\,{\it \_C1} \right ) -84\,\ln \left ( x \right ) +21}} \right \} \]