3.825   ODE No. 825

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

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

Mathematica: cpu = 0.183023 (sec), leaf count = 148 $$\text{Solve}[-\frac{19}{3}\text{RootSum}[-19{\mathrm{\#}\text{1}}^3+6\sqrt[3]{38}\mathrm{\#}\text{1}-19\mathrm{\&},\frac{\log (\frac{\frac{3xy(x)}{{(x^2+1)}^2}+\frac{x}{{(x^2+1)}^{3/2}}}{\sqrt[3]{38}\sqrt[3]{\frac{x^3}{{(x^2+1)}^{9/2}}}}-\mathrm{\#}\text{1})}{2\sqrt[3]{38}-19{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{{19}^{2/3}{\left(\frac{x^3}{{(x^2+1)}^{9/2}}\right)}^{2/3}{(x^2+1)}^3\log (x^2+1)}{9\sqrt[3]{2}{x}^2},y(x)]$$

Maple: cpu = 0.062 (sec), leaf count = 89 $$\{y\left(x\right)=\frac{19\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-1296{\int }^{\mathit{\_}\mathit{Z}}{(361{\mathit{\_}\mathit{a}}^3-432\mathit{\_}\mathit{a}+432)}^{-1}d\mathit{\_}\mathit{a}+2\ln (x^2+1)+3\mathit{\_}\mathit{C}\mathit{1})x^2-6x^2+19\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-1296{\int }^{\mathit{\_}\mathit{Z}}{(361{\mathit{\_}\mathit{a}}^3-432\mathit{\_}\mathit{a}+432)}^{-1}d\mathit{\_}\mathit{a}+2\ln (x^2+1)+3\mathit{\_}\mathit{C}\mathit{1})-6}{18}\frac{1}{\sqrt{x^2+1}}\}$$