3.707   ODE No. 707

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/16{(-\ln (-1+y\left(x\right))+\ln (1+y\left(x\right))+2\ln \left(x\right))}^{2}x{(1+y\left(x\right))}^2=0}}$$

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

Mathematica: cpu = 480.133469 (sec), leaf count = 334 $$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{2(K[2]+1)}+\frac{-{\log }^2(K[2]-1)-{\log }^2(K[2]+1)+2\log (K[2]+1)\log (K[2]-1)+16}{2({\log }^2(K[2]-1)+{\log }^2(K[2]+1)+K[2]({\log }^2(K[2]-1)+{\log }^2(K[2]+1)-2\log (K[2]+1)\log (K[2]-1)-16)-2\log (K[2]+1)\log (K[2]-1)+16)})dK[2]+{\int }_1^x-\frac{(y(x)+1)K[1](2\log (K[1])-\log (y(x)-1)+\log (y(x)+1){)}^2}{K[1{]}^2{\log }^2(y(x)-1)+K[1{]}^2{\log }^2(y(x)+1)+4y(x)K[1{]}^2{\log }^2(K[1])+y(x)K[1{]}^2{\log }^2(y(x)-1)+y(x)K[1{]}^2{\log }^2(y(x)+1)-4K[1{]}^2\log (y(x)-1)\log (K[1])+4K[1{]}^2\log (y(x)+1)\log (K[1])-2K[1{]}^2\log (y(x)-1)\log (y(x)+1)-4y(x)K[1{]}^2\log (y(x)-1)\log (K[1])+4y(x)K[1{]}^2\log (y(x)+1)\log (K[1])-2y(x)K[1{]}^2\log (y(x)-1)\log (y(x)+1)+4K[1{]}^2{\log }^2(K[1])-16y(x)+16}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.468 (sec), leaf count = 105 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{4\mathit{\_}\mathit{a}+4}{(\frac{x^2(\mathit{\_}\mathit{a}+1){(\ln (\mathit{\_}\mathit{a}-1))}^2}{4}-(\ln \left(x\right)+\frac{\ln (\mathit{\_}\mathit{a}+1)}{2})x^2(\mathit{\_}\mathit{a}+1)\ln (\mathit{\_}\mathit{a}-1)+\frac{x^2(\mathit{\_}\mathit{a}+1){(\ln (\mathit{\_}\mathit{a}+1))}^2}{4}+x^2\ln \left(x\right)(\mathit{\_}\mathit{a}+1)\ln (\mathit{\_}\mathit{a}+1)+x^2(\mathit{\_}\mathit{a}+1){(\ln \left(x\right))}^2-4\mathit{\_}\mathit{a}+4)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\frac{\ln \left(x\right)}{16}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$