3.971   ODE No. 971

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{(xy\left(x\right)+1)}^3}{x^5}=0}}$$

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

Mathematica: cpu = 0.101013 (sec), leaf count = 157 $$\text{Solve}[\frac{1}{3}\log (\frac{\frac{3}{x^3}+\frac{3y(x)}{x^2}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)-\frac{1}{6}\log (\frac{{(\frac{3}{x^3}+\frac{3y(x)}{x^2})}^2}{9{(-\frac{1}{x^6})}^{2/3}}-\frac{\frac{3}{x^3}+\frac{3y(x)}{x^2}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)+\frac{{\tan }^{-1}\left(\frac{\frac{2(\frac{3}{x^3}+\frac{3y(x)}{x^2})}{3\sqrt[3]{-\frac{1}{x^6}}}-1}{\sqrt{3}}\right)}{\sqrt{3}}=c_1-{(-\frac{1}{x^6})}^{2/3}{x}^3,y(x)]$$

Maple: cpu = 0.187 (sec), leaf count = 88 $$\{y\left(x\right)=\frac{\sqrt{3}}{6x}(\sqrt{3}\sqrt[3]{-x^{-6}}{x}^3+3\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-18x^3{(-x^{-6})}^{2/3}-6\mathit{\_}\mathit{Z}\sqrt{3}-\ln \left(\frac{{(\sqrt{3}+\tan \left(\mathit{\_}\mathit{Z}\right))}^6}{{({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}^3}\right)+18\mathit{\_}\mathit{C}\mathit{1})\right)x^3\sqrt[3]{-x^{-6}}-2\sqrt{3})\}$$