3.315   ODE No. 315

$$\boxed{{\displaystyle (2x{\left(y\left(x\right)\right)}^3-x^4)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^4+2x^{3}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.114515 (sec), leaf count = 368 $$\{\{y(x)\to \frac{\sqrt[3]{\frac{2}{3}}{e}^{c_1}x}{\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}+\frac{\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}{\sqrt[3]{2}{3}^{2/3}}\},\{y(x)\to -\frac{(1+i\sqrt{3})e^{c_1}x}{2^{2/3}\sqrt[3]{3}\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}{2\sqrt[3]{2}{3}^{2/3}}\},\{y(x)\to -\frac{(1-i\sqrt{3})e^{c_1}x}{2^{2/3}\sqrt[3]{3}\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{3}\sqrt{27x^6-4e^{3c_1}{x}^3}-9x^3}}{2\sqrt[3]{2}{3}^{2/3}}\}\}$$

Maple: cpu = 0.062 (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}})\}$$