2.270   ODE No. 270

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

$$x^2+(y(x{)}^2-x)y^{\prime }(x)-y(x)=0$$ ✓ Mathematica : cpu = 4.30963 (sec), leaf count = 326

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

✓ Maple : cpu = 0.028 (sec), leaf count = 319

$$\{y\left(x\right)=\frac{1}{2}({(-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x)\frac{1}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=-\frac{1}{4}((i{(-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}-4ix)\sqrt{3}+{(-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x)\frac{1}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=\frac{1}{4}(i{(-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}\sqrt{3}-4i\sqrt{3}x-{(-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}-4x)\frac{1}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}\}$$