3.748   ODE No. 748

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

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

Mathematica: cpu = 0.382549 (sec), leaf count = 285 $$\{\{y(x)\to \frac{2\sqrt[3]{2}(c_1+\log (x))}{\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}+\frac{\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}{3\sqrt[3]{2}}\},\{y(x)\to -\frac{\sqrt[3]{2}(1+i\sqrt{3})(c_1+\log (x))}{\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}{6\sqrt[3]{2}}\},\{y(x)\to -\frac{\sqrt[3]{2}(1-i\sqrt{3})(c_1+\log (x))}{\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{2916x^2-864(c_1+\log (x)){}^3}+54x}}{6\sqrt[3]{2}}\}\}$$

Maple: cpu = 0.078 (sec), leaf count = 497 $$\{y\left(x\right)=\frac{1}{3}\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}}-3\frac{-2/3\mathit{\_}\mathit{C}\mathit{1}-2/3\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}}},y\left(x\right)=-\frac{1}{6}\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{3}{2}(-\frac{2\mathit{\_}\mathit{C}\mathit{1}}{3}-\frac{2\ln \left(x\right)}{3})\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}}}-\frac{i}{2}\sqrt{3}(\frac{1}{3}\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}}+3\frac{-2/3\mathit{\_}\mathit{C}\mathit{1}-2/3\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}}}),y\left(x\right)=-\frac{1}{6}\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{3}{2}(-\frac{2\mathit{\_}\mathit{C}\mathit{1}}{3}-\frac{2\ln \left(x\right)}{3})\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}}}+\frac{i}{2}\sqrt{3}(\frac{1}{3}\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}}+3\frac{-2/3\mathit{\_}\mathit{C}\mathit{1}-2/3\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}}})\}$$