3.722   ODE No. 722

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{{\left(y\left(x\right)\right)}^3}{(-1+2y\left(x\right)\ln \left(x\right)-y\left(x\right))x}=0}}$$

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

Mathematica: cpu = 63.894114 (sec), leaf count = 491 $$\text{Solve}[\frac{\sqrt[3]{-2}((-2{)}^{2/3}-\frac{(1-2\log (x){)}^2{(-\frac{1}{(2\log (x)-1{)}^3})}^{2/3}(y(x)(5-4\log (x))+2)}{2\sqrt[3]{2}(y(x)(2\log (x)-1)-1)})(\frac{y(x)(4\log (x)-5)-2}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(2\log (x)-1{)}^3}}(2\log (x)-1)(y(x)(2\log (x)-1)-1)}+(-2{)}^{2/3})(-\log ((-2{)}^{2/3}-\frac{(1-2\log (x){)}^2{(-\frac{1}{(2\log (x)-1{)}^3})}^{2/3}(y(x)(5-4\log (x))+2)}{2\sqrt[3]{2}(y(x)(2\log (x)-1)-1)})(\frac{\sqrt[3]{-1}{(-\frac{1}{(2\log (x)-1{)}^3})}^{2/3}(1-2\log (x){)}^2(y(x)(4\log (x)-5)-2)}{y(x)(4\log (x)-2)-2}+1)+\log (\frac{y(x)(4\log (x)-5)-2}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(2\log (x)-1{)}^3}}(2\log (x)-1)(y(x)(2\log (x)-1)-1)}+(-2{)}^{2/3})(\frac{\sqrt[3]{-1}{(-\frac{1}{(2\log (x)-1{)}^3})}^{2/3}(1-2\log (x){)}^2(y(x)(4\log (x)-5)-2)}{y(x)(4\log (x)-2)-2}+1)-3)}{9(\frac{(y(x)(4\log (x)-5)-2{)}^3}{8(y(x)(2\log (x)-1)-1{)}^3}+\frac{3\sqrt[3]{-1}(y(x)(4\log (x)-5)-2)}{2(1-2\log (x){)}^4{(-\frac{1}{(2\log (x)-1{)}^3})}^{4/3}(y(x)(2\log (x)-1)-1)}+2)}=c_1+\frac{4}{9}{2}^{2/3}\log (x){(-\frac{1}{(2\log (x)-1{)}^3})}^{2/3}(1-2\log (x){)}^2,y(x)]$$

Maple: cpu = 0.281 (sec), leaf count = 96 $$\{y\left(x\right)=1{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2}{2x^4}\right)+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2)}{(2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(1/2\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2}{x^4}\right)+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2)}\ln \left(x\right)-{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2}{2x^4}\right)+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2)}+1)}^{-1}\}$$