ODE No. 971

$$y^{\prime }(x)=\frac{(xy(x)+1{)}^3}{x^5}$$ ✓ Mathematica : cpu = 0.287235 (sec), leaf count = 157

DSolve[Derivative[1][y][x] == (1 + x*y[x])^3/x^5,y[x],x]
 

$$\text{Solve}[\frac{1}{3}\log (\frac{\frac{3}{x^3}+\frac{3y(x)}{x^2}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)-\frac{1}{6}\log (\frac{{(\frac{3}{x^3}+\frac{3y(x)}{x^2})}^2}{9{(-\frac{1}{x^6})}^{2/3}}-\frac{\frac{3}{x^3}+\frac{3y(x)}{x^2}}{3\sqrt[3]{-\frac{1}{x^6}}}+1)+\frac{{\tan }^{-1}\left(\frac{\frac{2(\frac{3}{x^3}+\frac{3y(x)}{x^2})}{3\sqrt[3]{-\frac{1}{x^6}}}-1}{\sqrt{3}}\right)}{\sqrt{3}}=-{(-\frac{1}{x^6})}^{2/3}{x}^3+c_1,y(x)]$$ ✓ Maple : cpu = 0.279 (sec), leaf count = 86

dsolve(diff(y(x),x) = (x*y(x)+1)^3/x^5,y(x))
 

$$y\left(x\right)=\frac{(3\tan \left(\mathrm{RootOf}(-18x^3{(-\frac{1}{x^6})}^{\frac{2}{3}}-6\mathit{\text{\_Z}}\sqrt{3}-\ln \left(\frac{{(\sqrt{3}+\tan \left(\mathit{\text{\_Z}}\right))}^6}{{({\tan }^2\left(\mathit{\text{\_Z}}\right)+1)}^3}\right)+18c_1)\right)x^3{(-\frac{1}{x^6})}^{\frac{1}{3}}+\sqrt{3}(x^3{(-\frac{1}{x^6})}^{\frac{1}{3}}-2))\sqrt{3}}{6x}$$