2.613   ODE No. 613

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

$$y^{\prime }(x)=\frac{x^{2}F\left(\frac{y(x)-x\log (x)}{x}\right)+y(x)+x}{x}$$ ✓ Mathematica : cpu = 0.287117 (sec), leaf count = 226

$$\text{Solve}[{\int }_1^{y(x)}-\frac{xF\left(\frac{K[2]-x\log (x)}{x}\right){\int }_1^x(-\frac{K[2]F^{\prime }\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}{F{\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}^{2}K[1{]}^3}-\frac{F^{\prime }\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}{F{\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)}^{2}K[1{]}^2}+\frac{1}{F\left(\frac{K[2]-K[1]\log (K[1])}{K[1]}\right)K[1{]}^2})dK[1]+1}{xF\left(\frac{K[2]-x\log (x)}{x}\right)}dK[2]+{\int }_1^x(\frac{y(x)}{F\left(\frac{y(x)-K[1]\log (K[1])}{K[1]}\right)K[1{]}^2}+\frac{1}{F\left(\frac{y(x)-K[1]\log (K[1])}{K[1]}\right)K[1]}+1)dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.174 (sec), leaf count = 23

$$\{y\left(x\right)=(\ln \left(x\right)+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}{\left(F\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}))x\}$$