3.613   ODE No. 613

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

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

Mathematica: cpu = 818.937492 (sec), leaf count = 223 $$\text{Solve}[{\int }_1^{y(x)}-\frac{xF\left(\frac{K[2]-x\log (x)}{x}\right){\int }_1^x(-\frac{K[2]F^{\prime }\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}{K[1{]}^{3}F{\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}^2}-\frac{F^{\prime }\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}{K[1{]}^{2}F{\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}^2}+\frac{1}{K[1{]}^{2}F\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)})dK[1]+1}{xF\left(\frac{K[2]-x\log (x)}{x}\right)}dK[2]+{\int }_1^x(\frac{y(x)}{K[1{]}^{2}F\left(\frac{y(x)-K[1]\log (K[1])}{K[1]}\right)}+\frac{1}{K[1]F\left(\frac{y(x)-K[1]\log (K[1])}{K[1]}\right)}+1)dK[1]=c_1,y(x)]$$

Maple: cpu = 0.093 (sec), leaf count = 23 $$\{y\left(x\right)=(\ln \left(x\right)+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}))x\}$$