2.971   ODE No. 971

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

$$y^{\prime }(x)=\frac{(xy(x)+1{)}^3}{x^5}$$ ✓ Mathematica : cpu = 0.205106 (sec), leaf count = 157

$$\text{Solve}[\frac{1}{3}\log (\frac{\frac{3y(x)}{x^2}+\frac{3}{x^3}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)-\frac{1}{6}\log (\frac{{(\frac{3y(x)}{x^2}+\frac{3}{x^3})}^2}{9{(-\frac{1}{x^6})}^{2/3}}-\frac{\frac{3y(x)}{x^2}+\frac{3}{x^3}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)+\frac{{\tan }^{-1}\left(\frac{\frac{2(\frac{3y(x)}{x^2}+\frac{3}{x^3})}{3\sqrt[3]{-\frac{1}{x^6}}}-1}{\sqrt{3}}\right)}{\sqrt{3}}=-{(-\frac{1}{x^6})}^{2/3}{x}^3+c_1,y(x)]$$ ✓ Maple : cpu = 1.2 (sec), leaf count = 86

$$\{y\left(x\right)=\frac{\sqrt{3}}{6x}(3\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-18x^3{(-x^{-6})}^{2/3}-6\sqrt{3}\mathit{\_}\mathit{Z}-\ln \left(\frac{{(\sqrt{3}+\tan \left(\mathit{\_}\mathit{Z}\right))}^6}{{({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}^3}\right)+18\mathit{\_}\mathit{C}\mathit{1})\right)x^3\sqrt[3]{-x^{-6}}+\sqrt{3}(x^3\sqrt[3]{-x^{-6}}-2))\}$$