#### 2.735   ODE No. 735

$y'(x)=\frac {(2 y(x) \log (x)-1)^3}{x (-y(x)+2 y(x) \log (x)-1)}$ Mathematica : cpu = 11.4914 (sec), leaf count = 573

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {2 (2 \log (x) K[1]-K[1]-1)}{8 \log ^3(x) K[1]^3+4 \log (x) K[1]^3-2 K[1]^3-12 \log ^2(x) K[1]^2-2 K[1]^2+6 \log (x) K[1]-1}+2 \text {RootSum}\left [2 K[1]^3-2 \text {\#1} K[1]^2-\text {\#1}^3\& ,\frac {K[1] \log (2 K[1] \log (x)-\text {\#1}-1)-\log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1}}{2 K[1]^2+3 \text {\#1}^2}\& \right ]+\frac {\text {RootSum}\left [2 K[1]^3-2 \text {\#1} K[1]^2-\text {\#1}^3\& ,\frac {16 \log (x) K[1]^3-16 \log (x) \log (2 K[1] \log (x)-\text {\#1}-1) K[1]^3-24 \log (2 K[1] \log (x)-\text {\#1}-1) K[1]^3+24 K[1]^3+8 \log (2 K[1] \log (x)-\text {\#1}-1) K[1]^2+2 \log (x) \text {\#1} K[1]^2-2 \log (x) \log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1} K[1]^2+32 \log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1} K[1]^2-32 \text {\#1} K[1]^2-24 \log (x) \text {\#1}^2 K[1]+24 \log (x) \log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1}^2 K[1]+\log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1}^2 K[1]-\text {\#1}^2 K[1]+\log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1} K[1]-12 \log (2 K[1] \log (x)-\text {\#1}-1) \text {\#1}^2}{58 \log (x) K[1]^3-18 K[1]^3-54 \log (x) \text {\#1} K[1]^2-11 \text {\#1} K[1]^2-29 K[1]^2+18 \log (x) \text {\#1}^2 K[1]+27 \text {\#1}^2 K[1]+27 \text {\#1} K[1]-9 \text {\#1}^2}\& \right ]}{K[1]}\right )dK[1]-2 \left (y(x) \text {RootSum}\left [-\text {\#1}^3-2 \text {\#1} y(x)^2+2 y(x)^3\& ,\frac {y(x) \log (-\text {\#1}+2 y(x) \log (x)-1)-\text {\#1} \log (-\text {\#1}+2 y(x) \log (x)-1)}{3 \text {\#1}^2+2 y(x)^2}\& \right ]+\log (x)\right )=c_1,y(x)\right ]$ Maple : cpu = 0.216 (sec), leaf count = 78

$\left \{ y \left ( x \right ) ={\frac {71\,{\it RootOf} \left ( -82944\,\int ^{{\it \_Z}}\! \left ( 5041\,{{\it \_a}}^{3}-27648\,{\it \_a}+27648 \right ) ^{-1}{d{\it \_a}}-16\,\ln \left ( x \right ) +3\,{\it \_C1} \right ) -120}{ \left ( 142\,\ln \left ( x \right ) -71 \right ) {\it RootOf} \left ( -82944\,\int ^{{\it \_Z}}\! \left ( 5041\,{{\it \_a}}^{3}-27648\,{\it \_a}+27648 \right ) ^{-1}{d{\it \_a}}-16\,\ln \left ( x \right ) +3\,{\it \_C1} \right ) -240\,\ln \left ( x \right ) +48}} \right \}$