3.874   ODE No. 874

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{(-256a{x}^2+512+512{\left(y\left(x\right)\right)}^2+128y\left(x\right)a{x}^4+8a^2{x}^8+512{\left(y\left(x\right)\right)}^3+192x^{4}a{\left(y\left(x\right)\right)}^2+24y\left(x\right)a^2{x}^8+a^3{x}^{12})x}{512}=0}}$$

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

Mathematica: cpu = 0.067509 (sec), leaf count = 101 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{1}{8}(3a{x}^5+8x)+3xy(x)}{\sqrt[3]{29}\sqrt[3]{x^3}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{18}{29}^{2/3}{\left(x^3\right)}^{2/3},y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 40 $$\{y\left(x\right)=-\frac{a{x}^4}{8}-\frac{1}{3}+\frac{29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(x^2-162{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+6\mathit{\_}\mathit{C}\mathit{1})}{9}\}$$