3.299   ODE No. 299

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

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

Mathematica: cpu = 0.017002 (sec), leaf count = 371 $$\{\{y(x)\to -\frac{\sqrt[3]{\frac{2}{3}}{x}^2}{\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}-\frac{\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}{\sqrt[3]{2}{3}^{2/3}x}\},\{y(x)\to \frac{(1+i\sqrt{3})x^2}{2^{2/3}\sqrt[3]{3}\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}+\frac{(1-i\sqrt{3})\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}{2\sqrt[3]{2}{3}^{2/3}x}\},\{y(x)\to \frac{(1-i\sqrt{3})x^2}{2^{2/3}\sqrt[3]{3}\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}+\frac{(1+i\sqrt{3})\sqrt[3]{9c_1{x}^2+\sqrt{3}\sqrt{27c_1^2{x}^4-4x^9}}}{2\sqrt[3]{2}{3}^{2/3}x}\}\}$$

Maple: cpu = 0.125 (sec), leaf count = 327 $$\{y\left(x\right)=\frac{1}{6x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}+2\frac{x^2}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}},y\left(x\right)=-\frac{1}{12x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}-x^2\frac{1}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}}-\frac{i}{2}\sqrt{3}(\frac{1}{6x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}-2\frac{x^2}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}}),y\left(x\right)=-\frac{1}{12x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}-x^2\frac{1}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}}+\frac{i}{2}\sqrt{3}(\frac{1}{6x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}-2\frac{x^2}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}})\}$$