2.729   ODE No. 729

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

$$y^{\prime }(x)=\frac{(x-y(x))y(x)}{x(x-y(x{)}^3)}$$ ✓ Mathematica : cpu = 0.291467 (sec), leaf count = 327

$$\{\{y(x)\to \frac{\sqrt[3]{2}(-6\log (x)+6c_1)}{3\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}-\frac{\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}{3\sqrt[3]{2}}\},\{y(x)\to \frac{(1+i\sqrt{3})\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}{6\sqrt[3]{2}}-\frac{(1-i\sqrt{3})(-6\log (x)+6c_1)}{32^{2/3}\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}\},\{y(x)\to \frac{(1-i\sqrt{3})\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}{6\sqrt[3]{2}}-\frac{(1+i\sqrt{3})(-6\log (x)+6c_1)}{32^{2/3}\sqrt[3]{54x+\sqrt{2916x^2+4(-6\log (x)+6c_1){}^3}}}\}\}$$ ✓ Maple : cpu = 0.292 (sec), leaf count = 404

$$\{y\left(x\right)=\frac{1}{3}({(-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2})}^{\frac{2}{3}}+6\ln \left(x\right)-6\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2}}},y\left(x\right)=\frac{1}{6}((i{(-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2})}^{\frac{2}{3}}+6i\mathit{\_}\mathit{C}\mathit{1}-6i\ln \left(x\right))\sqrt{3}-{(-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2})}^{\frac{2}{3}}+6\mathit{\_}\mathit{C}\mathit{1}-6\ln \left(x\right))\frac{1}{\sqrt[3]{-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2}}},y\left(x\right)=-\frac{1}{6}((i{(-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2})}^{\frac{2}{3}}+6i\mathit{\_}\mathit{C}\mathit{1}-6i\ln \left(x\right))\sqrt{3}+{(-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2})}^{\frac{2}{3}}-6\mathit{\_}\mathit{C}\mathit{1}+6\ln \left(x\right))\frac{1}{\sqrt[3]{-27x+3\sqrt{-24{(\ln \left(x\right))}^3+72{(\ln \left(x\right))}^2\mathit{\_}\mathit{C}\mathit{1}-72\ln \left(x\right){\mathit{\_}\mathit{C}\mathit{1}}^2+24{\mathit{\_}\mathit{C}\mathit{1}}^3+81x^2}}}\}$$