\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/16\, \left ( -\ln \left ( -1+y \left ( x \right ) \right ) +\ln \left ( 1+y \left ( x \right ) \right ) +2\,\ln \left ( x \right ) \right ) ^{2}x \left ( 1+y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 480.133469 (sec), leaf count = 334 \[ \text {Solve}\left [\int _1^{y(x)} \left (\frac {1}{2 (K[2]+1)}+\frac {-\log ^2(K[2]-1)-\log ^2(K[2]+1)+2 \log (K[2]+1) \log (K[2]-1)+16}{2 \left (\log ^2(K[2]-1)+\log ^2(K[2]+1)+K[2] \left (\log ^2(K[2]-1)+\log ^2(K[2]+1)-2 \log (K[2]+1) \log (K[2]-1)-16\right )-2 \log (K[2]+1) \log (K[2]-1)+16\right )}\right ) \, dK[2]+\int _1^x -\frac {(y(x)+1) K[1] (2 \log (K[1])-\log (y(x)-1)+\log (y(x)+1))^2}{K[1]^2 \log ^2(y(x)-1)+K[1]^2 \log ^2(y(x)+1)+4 y(x) K[1]^2 \log ^2(K[1])+y(x) K[1]^2 \log ^2(y(x)-1)+y(x) K[1]^2 \log ^2(y(x)+1)-4 K[1]^2 \log (y(x)-1) \log (K[1])+4 K[1]^2 \log (y(x)+1) \log (K[1])-2 K[1]^2 \log (y(x)-1) \log (y(x)+1)-4 y(x) K[1]^2 \log (y(x)-1) \log (K[1])+4 y(x) K[1]^2 \log (y(x)+1) \log (K[1])-2 y(x) K[1]^2 \log (y(x)-1) \log (y(x)+1)+4 K[1]^2 \log ^2(K[1])-16 y(x)+16} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.468 (sec), leaf count = 105 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{4\,{\it \_a}+4} \left ( {\frac {{x}^{2} \left ( {\it \_a}+1 \right ) \left ( \ln \left ( {\it \_a}-1 \right ) \right ) ^{2}}{4}}- \left ( \ln \left ( x \right ) +{\frac {\ln \left ( {\it \_a}+1 \right ) }{2}} \right ) {x}^{2 } \left ( {\it \_a}+1 \right ) \ln \left ( {\it \_a}-1 \right ) +{\frac { {x}^{2} \left ( {\it \_a}+1 \right ) \left ( \ln \left ( {\it \_a}+1 \right ) \right ) ^{2}}{4}}+{x}^{2}\ln \left ( x \right ) \left ( {\it \_a}+1 \right ) \ln \left ( {\it \_a}+1 \right ) +{x}^{2} \left ( {\it \_a}+1 \right ) \left ( \ln \left ( x \right ) \right ) ^{2}-4\,{\it \_a }+4 \right ) ^{-1}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{ 16}}-{\it \_C1}=0 \right \} \]