3.589   ODE No. 589

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

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

Mathematica: cpu = 19.556483 (sec), leaf count = 242 $$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{K[2{]}^2(-F\left(\frac{1-\log (x)K[2]}{K[2]}\right)-1)}-{\int }_1^x(\frac{(-\frac{\log (K[1])}{K[2]}-\frac{1-K[2]\log (K[1])}{K[2{]}^2})F^{\prime }\left(\frac{1-K[2]\log (K[1])}{K[2]}\right)}{K[1](F\left(\frac{1-K[2]\log (K[1])}{K[2]}\right)+1)}-\frac{(-\frac{\log (K[1])}{K[2]}-\frac{1-K[2]\log (K[1])}{K[2{]}^2})F\left(\frac{1-K[2]\log (K[1])}{K[2]}\right)F^{\prime }\left(\frac{1-K[2]\log (K[1])}{K[2]}\right)}{K[1]{(F\left(\frac{1-K[2]\log (K[1])}{K[2]}\right)+1)}^2})dK[1])dK[2]+{\int }_1^x\frac{F\left(\frac{1-y(x)\log (K[1])}{y(x)}\right)}{K[1](F\left(\frac{1-y(x)\log (K[1])}{y(x)}\right)+1)}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.124 (sec), leaf count = 38 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{1}{{\mathit{\_}\mathit{a}}^2}{(F\left(\frac{1-\mathit{\_}\mathit{a}\ln \left(x\right)}{\mathit{\_}\mathit{a}}\right)+1)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$