3.297   ODE No. 297

$$\boxed{{\displaystyle 2x({\left(y\left(x\right)\right)}^2+5x^2)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^3-x^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.058007 (sec), leaf count = 216 $$\{\{y(x)\to \text{Root}[-{\mathrm{\#}\text{1}}^5+\frac{{\mathrm{\#}\text{1}}^2{e}^{3c_1}}{x^{3/2}}+3e^{3c_1}\sqrt{x}\mathrm{\&},1]\},\{y(x)\to \text{Root}[-{\mathrm{\#}\text{1}}^5+\frac{{\mathrm{\#}\text{1}}^2{e}^{3c_1}}{x^{3/2}}+3e^{3c_1}\sqrt{x}\mathrm{\&},2]\},\{y(x)\to \text{Root}[-{\mathrm{\#}\text{1}}^5+\frac{{\mathrm{\#}\text{1}}^2{e}^{3c_1}}{x^{3/2}}+3e^{3c_1}\sqrt{x}\mathrm{\&},3]\},\{y(x)\to \text{Root}[-{\mathrm{\#}\text{1}}^5+\frac{{\mathrm{\#}\text{1}}^2{e}^{3c_1}}{x^{3/2}}+3e^{3c_1}\sqrt{x}\mathrm{\&},4]\},\{y(x)\to \text{Root}[-{\mathrm{\#}\text{1}}^5+\frac{{\mathrm{\#}\text{1}}^2{e}^{3c_1}}{x^{3/2}}+3e^{3c_1}\sqrt{x}\mathrm{\&},5]\}\}$$

Maple: cpu = 0.219 (sec), leaf count = 29 $$\{y\left(x\right)={\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x^9\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^{45}-{\mathit{\_}\mathit{Z}}^{18}-6{\mathit{\_}\mathit{Z}}^9-9)\right)}^{\frac{9}{2}}x\}$$