3.398   ODE No. 398

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-3x{\left(y\left(x\right)\right)}^{2/3}\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+9{\left(y\left(x\right)\right)}^{5/3}=0}}$$

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

Mathematica: cpu = 0.737094 (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 = 2.402 (sec), leaf count = 137 $$\{\ln \left(x\right)+\frac{1}{6}\ln \left(\frac{y\left(x\right)}{x^6}\right)-\frac{1}{6}\ln (4\sqrt[3]{\frac{y\left(x\right)}{x^6}}-1)+1\sqrt{-4{\left(\frac{y\left(x\right)}{x^6}\right)}^{5/3}+{\left(\frac{y\left(x\right)}{x^6}\right)}^{\frac{4}{3}}}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{-4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1}\right){\left(\frac{y\left(x\right)}{x^6}\right)}^{-\frac{2}{3}}\frac{1}{\sqrt{-4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1}}-\frac{1}{6}\ln (16{\left(\frac{y\left(x\right)}{x^6}\right)}^{2/3}+4\sqrt[3]{\frac{y\left(x\right)}{x^6}}+1)+\frac{1}{6}\ln (64\frac{y\left(x\right)}{x^6}-1)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=\frac{x^6}{64}\}$$