3.882   ODE No. 882

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{(-108x^{3/2}-216-216{\left(y\left(x\right)\right)}^2+72x^{3}y\left(x\right)-6x^6-216{\left(y\left(x\right)\right)}^3+108x^3{\left(y\left(x\right)\right)}^2-18y\left(x\right)x^6+x^9)\sqrt{x}}{216}=0}}$$

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

Mathematica: cpu = 0.068009 (sec), leaf count = 119 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{1}{2}(2\sqrt{x}-x^{7/2})+3\sqrt{x}y(x)}{\sqrt[3]{29}\sqrt[3]{x^{3/2}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{2}{27}{29}^{2/3}\sqrt{x}{\left(x^{3/2}\right)}^{2/3},y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 41 $$\{y\left(x\right)=\frac{x^3}{6}-\frac{1}{3}+\frac{29}{9}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2x^{3/2}-243{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+9\mathit{\_}\mathit{C}\mathit{1})\}$$