2.795   ODE No. 795

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

$$y^{\prime }(x)=\frac{a^3+3a^{2}x+3a{x}^2+ay(x{)}^2+x^3+y(x{)}^3+xy(x{)}^2}{(a+x{)}^3}$$ ✓ Mathematica : cpu = 0.297673 (sec), leaf count = 106

$$\text{Solve}[57\text{RootSum}[-19{\mathrm{\#}\text{1}}^3+6\sqrt[3]{38}\mathrm{\#}\text{1}-19\mathrm{\&},\frac{\log (\frac{a+3y(x)+x}{\sqrt[3]{38}\sqrt[3]{\frac{1}{(a+x{)}^6}}(a+x{)}^3}-\mathrm{\#}\text{1})}{2\sqrt[3]{38}-19{\mathrm{\#}\text{1}}^2}\mathrm{\&}]+{38}^{2/3}{\left(\frac{1}{(a+x{)}^6}\right)}^{2/3}(a+x{)}^4\log (a+x)+9c_1=0,y(x)]$$

✓ Maple : cpu = 0.037 (sec), leaf count = 37

$$\{y\left(x\right)=-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}{({\mathit{\_}\mathit{a}}^3-{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}-1)}^{-1}d\mathit{\_}\mathit{a}+\ln (x+a)+\mathit{\_}\mathit{C}\mathit{1})(x+a)\}$$