3.270   ODE No. 270

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

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

Mathematica: cpu = 0.014502 (sec), leaf count = 327 $$\{\{y(x)\to -\frac{3\sqrt[3]{2}x}{\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}-\frac{\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}{3\sqrt[3]{2}}\},\{y(x)\to \frac{3(1+i\sqrt{3})x}{2^{2/3}\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}+\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}{6\sqrt[3]{2}}\},\{y(x)\to \frac{3(1-i\sqrt{3})x}{2^{2/3}\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}+\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{(81c_1+27x^3){}^2-2916x^3}+81c_1+27x^3}}{6\sqrt[3]{2}}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 402 $$\{y\left(x\right)=\frac{1}{2}\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+2\frac{x}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}},y\left(x\right)=-\frac{1}{4}\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-x\frac{1}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-2\frac{x}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}),y\left(x\right)=-\frac{1}{4}\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-x\frac{1}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-2\frac{x}{\sqrt[3]{-4x^3-12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+6x^3\mathit{\_}\mathit{C}\mathit{1}-4x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}})\}$$