2.874   ODE No. 874

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

$$y^{\prime }(x)=\frac{1}{512}x(24a^2{x}^{8}y(x)+a^3{x}^{12}+8a^2{x}^8+192a{x}^{4}y(x{)}^2+128a{x}^{4}y(x)-256a{x}^2+512y(x{)}^3+512y(x{)}^2+512)$$ ✓ Mathematica : cpu = 0.216223 (sec), leaf count = 101

$$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{1}{8}(3a{x}^5+8x)+3xy(x)}{\sqrt[3]{29}\sqrt[3]{x^3}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=\frac{1}{18}{29}^{2/3}{\left(x^3\right)}^{2/3}+c_1,y(x)]$$ ✓ Maple : cpu = 0.158 (sec), leaf count = 40

$$\{y\left(x\right)=-\frac{a{x}^4}{8}-\frac{1}{3}+\frac{29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x^2-162{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+6\mathit{\_}\mathit{C}\mathit{1})}{9}\}$$