\[ y'(x)=\frac {(2 y(x) \log (x)-1)^3}{x (-y(x)+2 y(x) \log (x)-1)} \] ✓ Mathematica : cpu = 1.13369 (sec), leaf count = 573
DSolve[Derivative[1][y][x] == (-1 + 2*Log[x]*y[x])^3/(x*(-1 - y[x] + 2*Log[x]*y[x])),y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {2 (2 \log (x) K[1]-K[1]-1)}{8 \log ^3(x) K[1]^3+4 \log (x) K[1]^3-2 K[1]^3-12 \log ^2(x) K[1]^2-2 K[1]^2+6 \log (x) K[1]-1}+2 \text {RootSum}\left [2 K[1]^3-2 \text {$\#$1} K[1]^2-\text {$\#$1}^3\& ,\frac {K[1] \log (2 K[1] \log (x)-\text {$\#$1}-1)-\log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}}{2 K[1]^2+3 \text {$\#$1}^2}\& \right ]+\frac {\text {RootSum}\left [2 K[1]^3-2 \text {$\#$1} K[1]^2-\text {$\#$1}^3\& ,\frac {16 \log (x) K[1]^3-16 \log (x) \log (2 K[1] \log (x)-\text {$\#$1}-1) K[1]^3-24 \log (2 K[1] \log (x)-\text {$\#$1}-1) K[1]^3+24 K[1]^3+8 \log (2 K[1] \log (x)-\text {$\#$1}-1) K[1]^2+2 \log (x) \text {$\#$1} K[1]^2-2 \log (x) \log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]^2+32 \log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]^2-32 \text {$\#$1} K[1]^2-24 \log (x) \text {$\#$1}^2 K[1]+24 \log (x) \log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2 K[1]+\log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2 K[1]-\text {$\#$1}^2 K[1]+\log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1} K[1]-12 \log (2 K[1] \log (x)-\text {$\#$1}-1) \text {$\#$1}^2}{58 \log (x) K[1]^3-18 K[1]^3-54 \log (x) \text {$\#$1} K[1]^2-11 \text {$\#$1} K[1]^2-29 K[1]^2+18 \log (x) \text {$\#$1}^2 K[1]+27 \text {$\#$1}^2 K[1]+27 \text {$\#$1} K[1]-9 \text {$\#$1}^2}\& \right ]}{K[1]}\right )dK[1]-2 \left (y(x) \text {RootSum}\left [-\text {$\#$1}^3-2 \text {$\#$1} y(x)^2+2 y(x)^3\& ,\frac {y(x) \log (-\text {$\#$1}+2 y(x) \log (x)-1)-\text {$\#$1} \log (-\text {$\#$1}+2 y(x) \log (x)-1)}{3 \text {$\#$1}^2+2 y(x)^2}\& \right ]+\log (x)\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.069 (sec), leaf count = 78
dsolve(diff(y(x),x) = (2*y(x)*ln(x)-1)^3/(-1+2*y(x)*ln(x)-y(x))/x,y(x))
\[y \left (x \right ) = \frac {71 \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1}\right )-120}{\left (142 \ln \left (x \right )-71\right ) \operatorname {RootOf}\left (-82944 \left (\int _{}^{\textit {\_Z}}\frac {1}{5041 \textit {\_a}^{3}-27648 \textit {\_a} +27648}d \textit {\_a} \right )-16 \ln \left (x \right )+3 c_{1}\right )-240 \ln \left (x \right )+48}\]