3.795   ODE No. 795

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

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

Mathematica: cpu = 0.156520 (sec), leaf count = 111 $$\text{Solve}[-\frac{19}{3}\text{RootSum}[-19{\mathrm{\#}\text{1}}^3+6\sqrt[3]{38}\mathrm{\#}\text{1}-19\mathrm{\&},\frac{\log (\frac{\frac{3y(x)}{(a+x{)}^3}+\frac{1}{(a+x{)}^2}}{\sqrt[3]{38}\sqrt[3]{\frac{1}{(a+x{)}^6}}}-\mathrm{\#}\text{1})}{2\sqrt[3]{38}-19{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=\frac{1}{9}{38}^{2/3}{\left(\frac{1}{(a+x{)}^6}\right)}^{2/3}(a+x{)}^4\log (a+x)+c_1,y(x)]$$

Maple: cpu = 0.032 (sec), leaf count = 37 $$\{y\left(x\right)=-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}{({\mathit{\_}\mathit{a}}^3-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}-1)}^{-1}d\mathit{\_}\mathit{a}+\ln (x+a)+\mathit{\_}\mathit{C}\mathit{1})(x+a)\}$$