2.271   ODE No. 271

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

$$(x^2+y(x{)}^2)y^{\prime }(x)+2x(y(x)+2x)=0$$ ✓ Mathematica : cpu = 0.262278 (sec), leaf count = 370

$$\{\{y(x)\to \frac{\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}{\sqrt[3]{2}}-\frac{\sqrt[3]{2}{x}^2}{\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}\},\{y(x)\to \frac{(1+i\sqrt{3})x^2}{2^{2/3}\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}-\frac{(1-i\sqrt{3})\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}{2\sqrt[3]{2}}\},\{y(x)\to \frac{(1-i\sqrt{3})x^2}{2^{2/3}\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}-\frac{(1+i\sqrt{3})\sqrt[3]{-4x^3+\sqrt{20x^6-8e^{3c_1}{x}^3+e^{6c_1}}+e^{3c_1}}}{2\sqrt[3]{2}}\}\}$$ ✓ Maple : cpu = 0.163 (sec), leaf count = 352

$$\{y\left(x\right)=(\frac{1}{2}\sqrt[3]{4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1}}-2\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2}{\sqrt[3]{4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1}}})\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=-\frac{1}{4}((4i\mathit{\_}\mathit{C}\mathit{1}{x}^2+i{(4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1})}^{\frac{2}{3}})\sqrt{3}-4\mathit{\_}\mathit{C}\mathit{1}{x}^2+{(4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1})}^{\frac{2}{3}})\frac{1}{\sqrt[3]{4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1}}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{1}{4}(4i\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}{x}^2+i\sqrt{3}{(4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1})}^{\frac{2}{3}}+4\mathit{\_}\mathit{C}\mathit{1}{x}^2-{(4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1})}^{\frac{2}{3}})\frac{1}{\sqrt[3]{4-16x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+4\sqrt{20{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^6-8x^3{\mathit{\_}\mathit{C}\mathit{1}}^{3/2}+1}}}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}}}\}$$