3.401   ODE No. 401

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

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

Mathematica: cpu = 0.353545 (sec), leaf count = 1093 $$\{\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},1]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},2]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},3]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},4]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},5]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+3{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-24{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+243e^{12c_1}+48{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},6]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},1]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},2]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},3]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},4]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},5]\},\{y(x)\to \text{Root}[-16e^{6c_1}{x}^6+243{\mathrm{\#}\text{1}}^4{x}^4+144e^{6c_1}\mathrm{\#}\text{1}{x}^4-1944{\mathrm{\#}\text{1}}^5{x}^2-378e^{6c_1}{\mathrm{\#}\text{1}}^2{x}^2+3e^{12c_1}+3888{\mathrm{\#}\text{1}}^6+216e^{6c_1}{\mathrm{\#}\text{1}}^3\mathrm{\&},6]\}\}$$

Maple: cpu = 0.452 (sec), leaf count = 656 $$\{y\left(x\right)=-3{(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}+1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6)}^2+2x(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}+1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6),y\left(x\right)=-3{(-1/12\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/12\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6-i/2\sqrt{3}(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2+2x(-1/12\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/12\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6-i/2\sqrt{3}(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}})),y\left(x\right)=-3{(-1/12\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/12\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6+i/2\sqrt{3}(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2+2x(-1/12\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/12\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+x/6+i/2\sqrt{3}(1/6\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/6\frac{x^2}{\sqrt[3]{-54\mathit{\_}\mathit{C}\mathit{1}+x^3+6\sqrt{-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+81{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))\}$$