3.724   ODE No. 724

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{{\left(y\left(x\right)\right)}^3}{(-1+y\left(x\right)\ln \left(x\right)-y\left(x\right))x}=0}}$$

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

Mathematica: cpu = 64.507191 (sec), leaf count = 420 $$\text{Solve}[\frac{\sqrt[3]{-2}(\frac{1-y(x)(\log (x)-4)}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+(-2{)}^{2/3})(\frac{2^{2/3}(y(x)(\log (x)-4)-1)}{\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+(-2{)}^{2/3})(-\log (\frac{1-y(x)(\log (x)-4)}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+(-2{)}^{2/3})(\frac{\sqrt[3]{-1}(1-y(x)(\log (x)-4))}{\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+1)+\log (\frac{2^{2/3}(y(x)(\log (x)-4)-1)}{\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+(-2{)}^{2/3})(\frac{\sqrt[3]{-1}(1-y(x)(\log (x)-4))}{\sqrt[3]{-\frac{1}{(\log (x)-1{)}^3}}(\log (x)-1)(y(x)(\log (x)-1)-1)}+1)-3)}{9(\frac{(y(x)(\log (x)-4)-1{)}^3}{(y(x)(\log (x)-1)-1{)}^3}+\frac{3\sqrt[3]{-1}(y(x)(\log (x)-4)-1)}{{(-\frac{1}{(\log (x)-1{)}^3})}^{4/3}(\log (x)-1{)}^4(y(x)(\log (x)-1)-1)}+2)}=c_1+\frac{1}{9}{2}^{2/3}{(-\frac{1}{(\log (x)-1{)}^3})}^{2/3}\log (x)(\log (x)-1{)}^2,y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 18 $$\{y\left(x\right)={(-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-2}x\right)+\ln \left(x\right)-2)}^{-1}\}$$