2.707   ODE No. 707

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)=\frac{1}{16}x(y(x)+1{)}^2(-\log (y(x)-1)+\log (y(x)+1)+2\log (x){)}^2$$ ✓ Mathematica : cpu = 4.95341 (sec), leaf count = 1391

$$\text{Solve}[{\int }_1^x-\frac{K[1](2\log (K[1])-\log (y(x)-1)+\log (y(x)+1){)}^2(y(x)+1)}{4{\log }^2(K[1])K[1{]}^2+{\log }^2(y(x)-1)K[1{]}^2+{\log }^2(y(x)+1)K[1{]}^2-4\log (K[1])\log (y(x)-1)K[1{]}^2+4\log (K[1])\log (y(x)+1)K[1{]}^2-2\log (y(x)-1)\log (y(x)+1)K[1{]}^2+4{\log }^2(K[1])y(x)K[1{]}^2+{\log }^2(y(x)-1)y(x)K[1{]}^2+{\log }^2(y(x)+1)y(x)K[1{]}^2-4\log (K[1])\log (y(x)-1)y(x)K[1{]}^2+4\log (K[1])\log (y(x)+1)y(x)K[1{]}^2-2\log (y(x)-1)\log (y(x)+1)y(x)K[1{]}^2-16y(x)+16}dK[1]+{\int }_1^{y(x)}(\frac{-4{\log }^2(x)x^2-{\log }^2(K[2]-1)x^2-{\log }^2(K[2]+1)x^2+4\log (x)\log (K[2]-1)x^2-4\log (x)\log (K[2]+1)x^2+2\log (K[2]-1)\log (K[2]+1)x^2+16}{2(4{\log }^2(x)x^2+{\log }^2(K[2]-1)x^2+{\log }^2(K[2]+1)x^2-4\log (x)\log (K[2]-1)x^2+4\log (x)\log (K[2]+1)x^2-2\log (K[2]-1)\log (K[2]+1)x^2+K[2](4{\log }^2(x)x^2+{\log }^2(K[2]-1)x^2+{\log }^2(K[2]+1)x^2-4\log (x)\log (K[2]-1)x^2+4\log (x)\log (K[2]+1)x^2-2\log (K[2]-1)\log (K[2]+1)x^2-16)+16)}-{\int }_1^x(-\frac{K[1](2\log (K[1])-\log (K[2]-1)+\log (K[2]+1){)}^2}{4K[2]{\log }^2(K[1])K[1{]}^2+4{\log }^2(K[1])K[1{]}^2+K[2]{\log }^2(K[2]-1)K[1{]}^2+{\log }^2(K[2]-1)K[1{]}^2+K[2]{\log }^2(K[2]+1)K[1{]}^2+{\log }^2(K[2]+1)K[1{]}^2-4K[2]\log (K[1])\log (K[2]-1)K[1{]}^2-4\log (K[1])\log (K[2]-1)K[1{]}^2+4K[2]\log (K[1])\log (K[2]+1)K[1{]}^2+4\log (K[1])\log (K[2]+1)K[1{]}^2-2K[2]\log (K[2]-1)\log (K[2]+1)K[1{]}^2-2\log (K[2]-1)\log (K[2]+1)K[1{]}^2-16K[2]+16}+\frac{K[1](K[2]+1)(4{\log }^2(K[1])K[1{]}^2+{\log }^2(K[2]-1)K[1{]}^2+{\log }^2(K[2]+1)K[1{]}^2-\frac{4K[2]\log (K[1])K[1{]}^2}{K[2]-1}-\frac{4\log (K[1])K[1{]}^2}{K[2]-1}+\frac{4K[2]\log (K[1])K[1{]}^2}{K[2]+1}+\frac{4\log (K[1])K[1{]}^2}{K[2]+1}+\frac{2K[2]\log (K[2]-1)K[1{]}^2}{K[2]-1}-4\log (K[1])\log (K[2]-1)K[1{]}^2+\frac{2\log (K[2]-1)K[1{]}^2}{K[2]-1}-\frac{2K[2]\log (K[2]-1)K[1{]}^2}{K[2]+1}-\frac{2\log (K[2]-1)K[1{]}^2}{K[2]+1}-\frac{2K[2]\log (K[2]+1)K[1{]}^2}{K[2]-1}+4\log (K[1])\log (K[2]+1)K[1{]}^2-2\log (K[2]-1)\log (K[2]+1)K[1{]}^2-\frac{2\log (K[2]+1)K[1{]}^2}{K[2]-1}+\frac{2K[2]\log (K[2]+1)K[1{]}^2}{K[2]+1}+\frac{2\log (K[2]+1)K[1{]}^2}{K[2]+1}-16)(2\log (K[1])-\log (K[2]-1)+\log (K[2]+1){)}^2}{{(4K[2]{\log }^2(K[1])K[1{]}^2+4{\log }^2(K[1])K[1{]}^2+K[2]{\log }^2(K[2]-1)K[1{]}^2+{\log }^2(K[2]-1)K[1{]}^2+K[2]{\log }^2(K[2]+1)K[1{]}^2+{\log }^2(K[2]+1)K[1{]}^2-4K[2]\log (K[1])\log (K[2]-1)K[1{]}^2-4\log (K[1])\log (K[2]-1)K[1{]}^2+4K[2]\log (K[1])\log (K[2]+1)K[1{]}^2+4\log (K[1])\log (K[2]+1)K[1{]}^2-2K[2]\log (K[2]-1)\log (K[2]+1)K[1{]}^2-2\log (K[2]-1)\log (K[2]+1)K[1{]}^2-16K[2]+16)}^2}-\frac{2K[1](K[2]+1)(\frac{1}{K[2]+1}-\frac{1}{K[2]-1})(2\log (K[1])-\log (K[2]-1)+\log (K[2]+1))}{4K[2]{\log }^2(K[1])K[1{]}^2+4{\log }^2(K[1])K[1{]}^2+K[2]{\log }^2(K[2]-1)K[1{]}^2+{\log }^2(K[2]-1)K[1{]}^2+K[2]{\log }^2(K[2]+1)K[1{]}^2+{\log }^2(K[2]+1)K[1{]}^2-4K[2]\log (K[1])\log (K[2]-1)K[1{]}^2-4\log (K[1])\log (K[2]-1)K[1{]}^2+4K[2]\log (K[1])\log (K[2]+1)K[1{]}^2+4\log (K[1])\log (K[2]+1)K[1{]}^2-2K[2]\log (K[2]-1)\log (K[2]+1)K[1{]}^2-2\log (K[2]-1)\log (K[2]+1)K[1{]}^2-16K[2]+16})dK[1]+\frac{1}{2(K[2]+1)})dK[2]=c_1,y(x)]$$ ✓ Maple : cpu = 0.368 (sec), leaf count = 105

$$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{4\mathit{\_}\mathit{a}+4}{(\frac{x^2(\mathit{\_}\mathit{a}+1){(\ln (\mathit{\_}\mathit{a}+1))}^2}{4}+(-\frac{\ln (\mathit{\_}\mathit{a}-1)}{2}+\ln \left(x\right))x^2(\mathit{\_}\mathit{a}+1)\ln (\mathit{\_}\mathit{a}+1)+\frac{x^2(\mathit{\_}\mathit{a}+1){(\ln (\mathit{\_}\mathit{a}-1))}^2}{4}-\ln \left(x\right)x^2(\mathit{\_}\mathit{a}+1)\ln (\mathit{\_}\mathit{a}-1)+x^2(\mathit{\_}\mathit{a}+1){(\ln \left(x\right))}^2-4\mathit{\_}\mathit{a}+4)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\frac{\ln \left(x\right)}{16}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$