3.621   ODE No. 621

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

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

Mathematica: cpu = 0.098513 (sec), leaf count = 445 $$\{\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},1]}-\sqrt{x}\},\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},2]}-\sqrt{x}\},\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},3]}-\sqrt{x}\},\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},4]}-\sqrt{x}\},\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},5]}-\sqrt{x}\},\{y(x)\to \frac{1}{\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},6]}-\sqrt{x}\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 59 $$\{y\left(x\right)=1(\sqrt{x}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^{18}\mathit{\_}\mathit{C}\mathit{1}-9x{\mathit{\_}\mathit{Z}}^6-6\sqrt{x}{\mathit{\_}\mathit{Z}}^3-1)\right)}^3+1){\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^{18}\mathit{\_}\mathit{C}\mathit{1}-9x{\mathit{\_}\mathit{Z}}^6-6\sqrt{x}{\mathit{\_}\mathit{Z}}^3-1)\right)}^{-3}\}$$