2.621   ODE No. 621

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

$$y^{\prime }(x)=\frac{1}{y(x)+\sqrt{x}}$$ ✓ Mathematica : cpu = 0.0578293 (sec), leaf count = 445

$$\{\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},1]}\},\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},2]}\},\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},3]}\},\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},4]}\},\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},5]}\},\{y(x)\to -\sqrt{x}+\frac{1}{\text{Root}[-24{\mathrm{\#}\text{1}}^4{x}^2+8{\mathrm{\#}\text{1}}^3{x}^{3/2}+{\mathrm{\#}\text{1}}^6(16x^3+16e^{12c_1})+9{\mathrm{\#}\text{1}}^{2}x-6\mathrm{\#}\text{1}\sqrt{x}+1\mathrm{\&},6]}\}\}$$ ✓ Maple : cpu = 1.143 (sec), leaf count = 59

$$\{y\left(x\right)=(\sqrt{x}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^{18}\mathit{\_}\mathit{C}\mathit{1}-9x{\mathit{\_}\mathit{Z}}^6-6\sqrt{x}{\mathit{\_}\mathit{Z}}^3-1)\right)}^3+1){\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^{18}\mathit{\_}\mathit{C}\mathit{1}-9x{\mathit{\_}\mathit{Z}}^6-6\sqrt{x}{\mathit{\_}\mathit{Z}}^3-1)\right)}^{-3}\}$$