2.398   ODE No. 398

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

$$y^{\prime }(x{)}^2-3xy(x{)}^{2/3}{y}^{\prime }(x)+9y(x{)}^{5/3}=0$$ ✓ Mathematica : cpu = 0.798309 (sec), leaf count = 258

$$\{\text{Solve}[-\frac{{(x^2-4\sqrt[3]{y(x)})}^{3/2}y(x{)}^2\log (y(x))}{6{((x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3})}^{3/2}}+\frac{\sqrt{(x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3}}\log (\sqrt{x^2-4\sqrt[3]{y(x)}}+x)}{\sqrt{x^2-4\sqrt[3]{y(x)}}y(x{)}^{2/3}}+\frac{1}{6}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{1}{6}(\frac{{(x^2-4\sqrt[3]{y(x)})}^{3/2}y(x{)}^2\log (y(x))}{{((x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3})}^{3/2}}+\log (y(x)))-\frac{\sqrt{(x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3}}\log (\sqrt{x^2-4\sqrt[3]{y(x)}}+x)}{\sqrt{x^2-4\sqrt[3]{y(x)}}y(x{)}^{2/3}}=c_1,y(x)]\}$$

✓ Maple : cpu = 2.427 (sec), leaf count = 138

$$\{\ln \left(x\right)+\frac{1}{6}\ln \left(\frac{y\left(x\right)}{x^6}\right)-\frac{1}{6}\ln (4\sqrt[3]{\frac{y\left(x\right)}{x^6}}-1)-1\sqrt{-4{\left(\frac{y\left(x\right)}{x^6}\right)}^{5/3}+{\left(\frac{y\left(x\right)}{x^6}\right)}^{\frac{4}{3}}}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{-4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1}\right){\left(\frac{y\left(x\right)}{x^6}\right)}^{-\frac{2}{3}}\frac{1}{\sqrt{-4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1}}-\frac{1}{6}\ln (16{\left(\frac{y\left(x\right)}{x^6}\right)}^{2/3}+4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1)+\frac{1}{6}\ln (64\frac{y\left(x\right)}{x^6}-1)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=\frac{x^6}{64}\}$$