#### 2.706   ODE No. 706

$y'(x)=-\frac {1}{8} x (y(x)+1)^2 (-\log (y(x)-1)+\log (y(x)+1)+2 \log (x))$ Mathematica : cpu = 40.2192 (sec), leaf count = 610

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {-2 \log (x) x^2+\log (K[2]-1) x^2-\log (K[2]+1) x^2-8}{2 \left (2 \log (x) x^2-\log (K[2]-1) x^2+\log (K[2]+1) x^2+K[2] \left (2 \log (x) x^2-\log (K[2]-1) x^2+\log (K[2]+1) x^2+8\right )-8\right )}-\int _1^x\left (-\frac {K[1] (K[2]+1) \left (\frac {1}{K[2]+1}-\frac {1}{K[2]-1}\right )}{2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8}-\frac {K[1] (2 \log (K[1])-\log (K[2]-1)+\log (K[2]+1))}{2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8}+\frac {K[1] (K[2]+1) (2 \log (K[1])-\log (K[2]-1)+\log (K[2]+1)) \left (-\frac {K[2] K[1]^2}{K[2]-1}+2 \log (K[1]) K[1]^2-\log (K[2]-1) K[1]^2+\log (K[2]+1) K[1]^2-\frac {K[1]^2}{K[2]-1}+\frac {K[2] K[1]^2}{K[2]+1}+\frac {K[1]^2}{K[2]+1}+8\right )}{\left (2 K[2] \log (K[1]) K[1]^2+2 \log (K[1]) K[1]^2-K[2] \log (K[2]-1) K[1]^2-\log (K[2]-1) K[1]^2+K[2] \log (K[2]+1) K[1]^2+\log (K[2]+1) K[1]^2+8 K[2]-8\right )^2}\right )dK[1]+\frac {1}{2 (K[2]+1)}\right )dK[2]+\int _1^x-\frac {K[1] (2 \log (K[1])-\log (y(x)-1)+\log (y(x)+1)) (y(x)+1)}{2 \log (K[1]) K[1]^2-\log (y(x)-1) K[1]^2+\log (y(x)+1) K[1]^2+2 \log (K[1]) y(x) K[1]^2-\log (y(x)-1) y(x) K[1]^2+\log (y(x)+1) y(x) K[1]^2+8 y(x)-8}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.464 (sec), leaf count = 65

$\left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!-{\frac {1}{2\,{\it \_a}+2} \left ( -{\frac {{x}^{2} \left ( {\it \_a}+1 \right ) \ln \left ( {\it \_a}-1 \right ) }{2}}+{\frac {{x}^{2} \left ( {\it \_a}+1 \right ) \ln \left ( {\it \_a}+1 \right ) }{2}}+{x}^{2} \left ( {\it \_a}+1 \right ) \ln \left ( x \right ) +4\,{\it \_a}-4 \right ) ^{-1}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{8}}-{\it \_C1}=0 \right \}$