3.311   ODE No. 311

$$\boxed{{\displaystyle (20{\left(y\left(x\right)\right)}^3-3x{\left(y\left(x\right)\right)}^2+6x^{2}y\left(x\right)+3x^3)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^3+6x{\left(y\left(x\right)\right)}^2+9x^{2}y\left(x\right)+4x^3=0}}$$

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

Mathematica: cpu = 0.051506 (sec), leaf count = 2201 $$\{\{y(x)\to \frac{x}{20}+\frac{1}{2}\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}-\frac{1}{2}\sqrt{-\frac{659x^3}{500\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}}-\frac{39x^2}{50}-\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}-\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}\},\{y(x)\to \frac{x}{20}+\frac{1}{2}\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}+\frac{1}{2}\sqrt{-\frac{659x^3}{500\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}}-\frac{39x^2}{50}-\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}-\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}\},\{y(x)\to \frac{x}{20}-\frac{1}{2}\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}-\frac{1}{2}\sqrt{\frac{659x^3}{500\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}}-\frac{39x^2}{50}-\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}-\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}\},\{y(x)\to \frac{x}{20}-\frac{1}{2}\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}+\frac{1}{2}\sqrt{\frac{659x^3}{500\sqrt{-\frac{39x^2}{100}+\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}+\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}}-\frac{39x^2}{50}-\frac{\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}{5\sqrt[3]{2}{3}^{2/3}}-\frac{2\sqrt[3]{\frac{2}{3}}(13x^4-10e^{c_1})}{5\sqrt[3]{99x^6+351e^{c_1}{x}^2+\sqrt{3}\sqrt{-67037x^{12}+185406e^{c_1}{x}^8-83733e^{2c_1}{x}^4+32000e^{3c_1}}}}}\}\}$$

Maple: cpu = 0.062 (sec), leaf count = 50 $$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x^4{\mathit{\_}\mathit{C}\mathit{1}}^4+3x^3{\mathit{\_}\mathit{C}\mathit{1}}^3\mathit{\_}\mathit{Z}+3{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2{x}^2-\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{3}x+5{\mathit{\_}\mathit{Z}}^4-1)}{\mathit{\_}\mathit{C}\mathit{1}}\}$$