3.264   ODE No. 264

$$\boxed{{\displaystyle 2x(x^{3}y\left(x\right)+1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(3x^{3}y\left(x\right)-1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.341043 (sec), leaf count = 680 $$\{\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},1]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},2]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},3]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},4]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},5]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},6]\},\{y(x)\to \text{Root}[81{\mathrm{\#}\text{1}}^7{e}^{\frac{21c_1}{2}}{x}^{12}+756{\mathrm{\#}\text{1}}^6{e}^{\frac{21c_1}{2}}{x}^9+2646{\mathrm{\#}\text{1}}^5{e}^{\frac{21c_1}{2}}{x}^6+4116{\mathrm{\#}\text{1}}^4{e}^{\frac{21c_1}{2}}{x}^3+2401{\mathrm{\#}\text{1}}^3{e}^{\frac{21c_1}{2}}-x^{3/2}\mathrm{\&},7]\}\}$$

Maple: cpu = 0.390 (sec), leaf count = 574 $$\{y\left(x\right)=\frac{-40353607{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{91}\mathit{\_}\mathit{C}\mathit{1}+756315{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{84}{x}^7+51883209{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{70}\mathit{\_}\mathit{C}\mathit{1}-108045{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{63}{x}^7-29647548{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{49}\mathit{\_}\mathit{C}\mathit{1}+9261{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{42}{x}^7+5764801{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{28}\mathit{\_}\mathit{C}\mathit{1}-441{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{21}{x}^7-352947{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^7\mathit{\_}\mathit{C}\mathit{1}+9x^7}{3x^3{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^7(5764801\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{84}-61740{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{77}{x}^7-6588344\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{63}+6615{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{56}{x}^7+3294172\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{42}-378{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{35}{x}^7-605052{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{21}\mathit{\_}\mathit{C}\mathit{1}+9{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(9x^7{\mathit{\_}\mathit{Z}}^{98}-49\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{42}+14\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{21}-\mathit{\_}\mathit{C}\mathit{1})\right)}^{14}{x}^7+36015\mathit{\_}\mathit{C}\mathit{1})}\}$$