2.778   ODE No. 778

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

$$y^{\prime }(x)=\frac{x^{9}y(x{)}^3+x^{6}y(x{)}^2-3x^{2}y(x)+1}{x^3}$$ ✓ Mathematica : cpu = 0.139763 (sec), leaf count = 95

$$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{3x^{6}y(x)+x^3}{\sqrt[3]{29}\sqrt[3]{x^9}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=\frac{{29}^{2/3}{\left(x^9\right)}^{2/3}}{9x^5}+c_1,y(x)]$$ ✓ Maple : cpu = 0.106 (sec), leaf count = 37

$$\{y\left(x\right)=\frac{-3+29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+x+3\mathit{\_}\mathit{C}\mathit{1})}{9x^3}\}$$