2.315   ODE No. 315

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

$$(2\text{Global}\stackrel{`}{}\text{x}\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}{)}^3-{\text{Global}\stackrel{`}{}\text{x}}^4){\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})+2{\text{Global}\stackrel{`}{}\text{x}}^3\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})-\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}{)}^4=0$$ ✓ Mathematica : cpu = 0.108128 (sec), leaf count = 368

$$\{\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to \frac{\sqrt[3]{\frac{2}{3}}{e}^{c_1}\text{Global}\stackrel{`}{}\text{x}}{\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}+\frac{\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}{\sqrt[3]{2}{3}^{2/3}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{(1+i\sqrt{3})e^{c_1}\text{Global}\stackrel{`}{}\text{x}}{2^{2/3}\sqrt[3]{3}\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}{2\sqrt[3]{2}{3}^{2/3}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{(1-i\sqrt{3})e^{c_1}\text{Global}\stackrel{`}{}\text{x}}{2^{2/3}\sqrt[3]{3}\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{3}\sqrt{27{\text{Global}\stackrel{`}{}\text{x}}^6-4e^{3c_1}{\text{Global}\stackrel{`}{}\text{x}}^3}-9{\text{Global}\stackrel{`}{}\text{x}}^3}}{2\sqrt[3]{2}{3}^{2/3}}\}\}$$

✓ Maple : cpu = 0.088 (sec), leaf count = 447

$$\{y\left(x\right)=\frac{\sqrt[3]{12}}{6\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}+\frac{x{12}^{\frac{2}{3}}}{6}\frac{1}{\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}},y\left(x\right)=-\frac{\sqrt[3]{12}}{12\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}-\frac{x{12}^{\frac{2}{3}}}{12}\frac{1}{\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{i}{2}\sqrt{3}(\frac{\sqrt[3]{12}}{6\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}-\frac{x{12}^{\frac{2}{3}}}{6}\frac{1}{\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}}),y\left(x\right)=-\frac{\sqrt[3]{12}}{12\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}-\frac{x{12}^{\frac{2}{3}}}{12}\frac{1}{\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}}+\frac{i}{2}\sqrt{3}(\frac{\sqrt[3]{12}}{6\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}-\frac{x{12}^{\frac{2}{3}}}{6}\frac{1}{\sqrt[3]{x(-9x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{3}\sqrt{\frac{x(27x^3{\mathit{\_}\mathit{C}\mathit{1}}^3-4)}{\mathit{\_}\mathit{C}\mathit{1}}}){\mathit{\_}\mathit{C}\mathit{1}}^2}})\}$$