3.865   ODE No. 865

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

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

Mathematica: cpu = 150.792648 (sec), leaf count = 84 $$\text{Solve}[{\int }_1^x(-\frac{f(K[1])}{\log (K[1])}-\frac{\log (y(x)-1)}{K[1]{\log }^2(K[1])})dK[1]+{\int }_1^{y(x)}(\frac{1}{\log (x)(K[2]-1)}-{\int }_1^x-\frac{1}{K[1](K[2]-1){\log }^2(K[1])}dK[1])dK[2]=c_1,y(x)]$$

Maple: cpu = 0.156 (sec), leaf count = 23 $$\{y\left(x\right)={\mathrm{e}}^{\int \frac{f\left(x\right)}{\ln \left(x\right)}\mathrm{d}x\ln \left(x\right)}{x}^{\mathit{\_}\mathit{C}\mathit{1}}+1\}$$