2.299   ODE No. 299

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

$$(3xy(x{)}^2-x^2)y^{\prime }(x)+y(x{)}^3-2xy(x)=0$$ ✓ Mathematica : cpu = 0.0224674 (sec), leaf count = 328

$$\{\{y(x)\to -\frac{\sqrt[3]{2}(9c_1{x}^2+\sqrt{81c_1^2{x}^4-12x^9}){}^{2/3}+2\sqrt[3]{3}{x}^3}{6^{2/3}x\sqrt[3]{9c_1{x}^2+\sqrt{81c_1^2{x}^4-12x^9}}}\},\{y(x)\to \frac{\sqrt[3]{3}(1-i\sqrt{3})(18c_1{x}^2+2\sqrt{81c_1^2{x}^4-12x^9}){}^{2/3}+2\sqrt[3]{2}\sqrt[6]{3}(\sqrt{3}+3i)x^3}{12x\sqrt[3]{9c_1{x}^2+\sqrt{81c_1^2{x}^4-12x^9}}}\},\{y(x)\to \frac{\sqrt[3]{3}(1+i\sqrt{3})(18c_1{x}^2+2\sqrt{81c_1^2{x}^4-12x^9}){}^{2/3}+2\sqrt[3]{2}\sqrt[6]{3}(\sqrt{3}-3i)x^3}{12x\sqrt[3]{9c_1{x}^2+\sqrt{81c_1^2{x}^4-12x^9}}}\}\}$$

✓ Maple : cpu = 0.238 (sec), leaf count = 276

$$\{y\left(x\right)=-\frac{{12}^{\frac{2}{3}}}{144x}((-12i{x}^3+i{\left((12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2\right)}^{\frac{2}{3}})\sqrt{3}+12x^3+{\left((12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2\right)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{(\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+9\mathit{\_}\mathit{C}\mathit{1})x^2}},y\left(x\right)=\frac{{12}^{\frac{2}{3}}}{144x}(-12i\sqrt{3}{x}^3+i\sqrt{3}{\left((12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2\right)}^{\frac{2}{3}}-12x^3-{\left((12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2\right)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{(\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+9\mathit{\_}\mathit{C}\mathit{1})x^2}},y\left(x\right)=\frac{1}{6x}\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}+2\frac{x^2}{\sqrt[3]{(12\sqrt{-12x^5+81{\mathit{\_}\mathit{C}\mathit{1}}^2}+108\mathit{\_}\mathit{C}\mathit{1})x^2}}\}$$