2.748   ODE No. 748

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

$$y^{\prime }(x)=\frac{y(x)(y(x)+x)}{x(y(x{)}^3+x)}$$ ✓ Mathematica : cpu = 0.308037 (sec), leaf count = 285

$$\{\{y(x)\to \frac{2\sqrt[3]{2}(\log (x)+c_1)}{\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}+\frac{\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}{3\sqrt[3]{2}}\},\{y(x)\to -\frac{\sqrt[3]{2}(1+i\sqrt{3})(\log (x)+c_1)}{\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}-\frac{(1-i\sqrt{3})\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}{6\sqrt[3]{2}}\},\{y(x)\to -\frac{\sqrt[3]{2}(1-i\sqrt{3})(\log (x)+c_1)}{\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}-\frac{(1+i\sqrt{3})\sqrt[3]{54x+\sqrt{2916x^2-864(\log (x)+c_1){}^3}}}{6\sqrt[3]{2}}\}\}$$ ✓ Maple : cpu = 0.278 (sec), leaf count = 404

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